A Study to Investigate the Efficacy, Safety and Tolerability of Four Different Doses of BI 409306 Compared to Placebo Given for 12 Weeks in Patients With Schizophrenia on Stable Antipsychotic Treatment.

Inclusion criteria: 1. Patients with established diagnoses of schizophrenia (per Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5)) with the following clinical features: a) Clinically stable and are in the residual (non-acute) phase of their illness for at least 8 weeks b) Current antipsychotic and concomitant psychotropic medications must meet the criteria below: b)-1 Maintained on current atypical (second generation) antipsychotic medications (in any approved dosage form) other than Clozapine and on current dose for at least 8 weeks prior to randomisation, and/or b)-2 Maintained on current typical (first generation) antipsychotic medications and on current dose for at least 6 months, optionally combined with anticholinergics if treated with a stable dose for at least 6 months prior to randomisation, and/or b)-3 Maintained on current concomitant psychotropic medications other than anticholinergics, antiepileptics and lithium, and on current dose for at least 8 weeks prior to randomisation. Antiepileptics and lithium are allowed if initiated at least 6 months prior to randomisation. b)-4 Anticholinergics, antiepileptics and lithium have been washed out for at least 6 months prior to randomisation if the treatments that patients were using before entering the clinical trial are discontinued. c) Have no more than a "moderate" severity rating on hallucinations and delusions (Positive and Negative Syndrome Scale (PANSS)-positive syndrome Hallucinatory Behavior item score \< =4 and Delusions item score \< = 4) d) Have no more than a "moderate" severity rating on positive formal thought disorder (PANSS-positive syndrome Conceptual Disorganization item score \< = 4) e) Have a minimal level of extrapyramidal symptoms (Simpson-Angus Scale total score \< 6) and depressive symptoms (PANSS-general psychopathology syndrome Depression item score \< = 4) 2. Male or female patients age 18 to 55 years 3. Patients must exhibit reliability, physiologic capability, and an educational level sufficient to comply with all protocol procedures,in the investigator's opinion. 4. Signed and dated written informed consent by date of Visit 1 in accordance with GCP and the local legislation. If the patient needs a legal representative, then this legal representative must give written informed consent as well. 5. Patients must have an identified informant who will be consistent throughout the study. The informant must interact with the subject at least 2 times a week. Note: Informant ratings are needed for SCoRS global ratings at Randomisation Visit (Visit 2) and (early) End of Treatment Visit. In person informant ratings on the study visits are preferred whenever possible. However, if the informant is not available for in person ratings, telephone interview is acceptable. The informant must be available for a telephone interview at Visit 2 and (e)EOT Visit. Exclusion criteria: 1. Patient treated with more than two antipsychotic medications (including more than two dosage forms) 2. Patient's cognitive impairment severity compromises the validity of the cognitive outcome measures, in the clinical judgment of the investigator 3. Any suicidal behavior in the past 2 years (i.e. actual attempt, interrupted attempt, aborted attempt, or preparatory acts or behavior) 4. Any suicidal ideation of type 4 or 5 in the Columbia Suicidal Severity Rating Scale (C-SSRS) in the past 3 months (i.e. active suicidal thought with intent but without specific plan, or active suicidal thought with plan and intent) 5. In the judgment of the investigator, any clinically significant finding of the medical examination (including BP, PR and ECG) or laboratory value deviating from normal or any evidence of a clinically significant concomitant disease or any other clinical condition that would jeopardize a patient's safety while participating in the clinical trial 6. History or diagnosis of symptomatic and unstable/uncontrolled gastrointestinal, hepatic, renal, respiratory, cardiovascular, metabolic, immunological, hematological or hormonal disorders 7. For female patients: Pre-menopausal women (last menstruation \< =1 year prior to informed consent) who: * are nursing or pregnant or * are of child-bearing potential and are not practicing an acceptable method of birth control, or do not plan to continue using this method throughout the trial until 28 days after the last treatment administration, and do not agree to submit to periodic pregnancy testing during participation in the trial. Acceptable methods of birth control include tubal ligation, vasectomized partner, transdermal patch, intra uterine devices/systems (IUDs/IUSs), combined estrogen-progestin oral contraceptives as well as implantable or injectable hormonal contraceptives. Complete sexual abstinence (if acceptable by local health authorities) is allowed when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptom-thermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception. Double barrier methods are permissible (if acceptable by local health authorities, note that this is not an acceptable method in EU countries). For male patients: Men who are able to father a child, unwilling to be abstinent or use adequate contraception for the duration of study participation and for at least 28 days after treatment has ended. 8. Known history of HIV infection 9. Diseases of the central nervous system (including but not limited to any kind of seizures, stroke or any psychiatric disorders other than schizophrenia) 10. Any subject who on the Mini-international neuropsychiatric Interview (M.I.N.I.) has a categorical diagnosis of another current major psychiatric disorder. 11. History of malignancy within the last 5 years, except for basal cell carcinoma 12. Planned elective surgery requiring general anaesthesia, or hospitalisation for more than 1 day during the study period 13. Significant history of drug dependence or abuse (including alcohol, as defined in DSM-5-substance use disorder or in the opinion of the investigator) within the last two years prior to informed consent, or a positive urine drug screen for cocaine, opioid, PCP, amphetamine, heroin, or marijuana at screening 14. Patient needs to take long-acting hypnotics and anxiolytics (i.e. Diazepam) 15. Patients taking medications that are known to be strong or moderate CYP3A4 inhibitors 16. Participation in another trial with an investigational drug or procedure within 30 days or 6 half-lives (whichever is longer) or participation in another trial with any cognitive-enhancing therapy or procedure within 90 days prior to screening 17. Previous participation in any BI 409306 study 18. Not fluent in the language of the batteries/questionnaires which will be used in the country