This Study Tests Whether BI 425809 Together With Brain Training Using a Computer Improves Mental Functioning in Patients With Schizophrenia

Inclusion Criteria: * Signed and dated written informed consent in accordance with ICH Harmonized Tripartite Guideline for Good Clinical Practice (ICH-GCP) and local legislation prior to admission to the trial. * Male or female patients who are 18-50 years (inclusive) of age at time of consent. * Established schizophrenia (as per DSM-5) with the following clinical features: * Outpatient, with no hospitalization for worsening of schizophrenia within 3 months prior to randomization * Psychiatrically stable without symptom exacerbation within 3 months prior to randomization * PANSS score ≤ 5 on positive items P1, P3-P7 and ≤ 4 on positive item P2 at Visit 1, and confirmed at Visit 2 * Patients must be on stable antipsychotic treatment; also, current antipsychotic medications and concomitant anticholinergics, antiepileptics, lithium and allowed antidepressants must meet the criteria below: * Patients must take 1 and may take up to 2 antipsychotics (typical and/or atypical), except for clozapine * Patients must be stable on current antipsychotics, anticholinergics, antiepileptics, lithium and allowed antidepressants for at least 3 months prior to randomization and be on current dose for at least 30 days prior to randomization o Patients on Long-Acting Injectable (LAI) antipsychotics should be on the same medication and dose for at least 3 months prior to randomization * Women of childbearing potential (WOCBP)2 must be ready and able to use highly effective methods of birth control per Non-Clinical Safety Studies for the Conduct of Human Clinical Trials and Marketing Authorization for Pharmaceuticals (ICH M3 (R2)) that result in a low failure rate of less than 1% per year when used consistently and correctly. A list of contraception methods meeting these criteria is provided in Section 4.2.2.3. Such methods should be used throughout the trial, and for a period of at least 35 days after last trial drug intake, and the patient must agree to periodic pregnancy testing during participation in the trial. * Patients must demonstrate their ability to properly use the CCT device and program, as well as be compliant with CCT run-in (defined as completing at least 2 hours per week for two weeks, totalling 4 hours CCT, during the screening period)3. * Patients must be able to comply with all protocol procedures, in the investigator's opinion. * Patients must have a study partner who will preferably be consistent throughout the study. It is recommended that the study partner should interact (in-person or telephone) with the subject at least 2 times a week. Exclusion Criteria: * Patients who have a categorical diagnosis of another current major psychiatric disorder on the Mini-International Neuropsychiatric Interview (M.I.N.I.). * Diseases of the central nervous system (CNS) that may impact the assessment of the cognitive tests as per investigator's opinion. A movement disorder due to antipsychotic treatment not currently controlled with anti- EPS treatment or another movement disorder (e.g. Parkinson´s disease). * Patients with a history of participating in any formal cognitive remediation program for 10 or more training sessions. * Patients who were treated with any of the following medications within the last 6 months prior to randomization: * Bitopertin, BI 409306, encenicline or other investigational drug testing effects on cognition in schizophrenia * Clozapine (atypical antipsychotic medication) * Sarcosine, cycloserine, serine and glycine * Stimulants (e.g. methylphenidate, dextroamphetamine, modafinil) * Tricyclic antidepressants * Patients receiving any other investigational drug (other than a potential cognitive enhancing drug) within 30 days or 6 half-lives (whichever is longer) prior to randomization. For investigational LAI antipsychotics, the last injection must be at least 3 months or two administration cycles (i.e. 6 months if administration is every 3 months) prior to randomization, whichever is longer. * Patients who have participated in a clinical trial with repeated assessments (i.e. a single assessment is not exclusionary) with the MATRICS Consensus Cognitive Battery (MCCB) within the last 6 months prior to randomization. * Patients who required a change in ongoing benzodiazepine or sleep medication dose or regimen within the last 30 days prior to randomization. * Patients with known active infection with SARS-CoV-2 within the last 30 days prior to randomization. * Other exclusion criteria apply