This is a randomised controlled trial which investigates the effectiveness of CARMS (Cognitive AppRoaches to coMbatting Suicidality) therapy in reducing suicidal thoughts and how well CARMS works in practice within the NHS. The trial will compare two groups of people with psychosis who are using NHS mental health services. One group will carry on with their usual treatment. The other group will be offered 24 weekly sessions of CARMS therapy, plus their usual treatment.