Theoretical properties of computer programs have been the object of considerable study in recent years. In this paper we consider the problem of joining - or composing - one program with another. We study basic properties of compositions within a theoretical model for parallel computation which is closely related to parallel program schemata. In particular, we introduce the notion of finishing schemata which have distinguished starting and ending states. A relation between parallel program schemata and finishing schemata is developed which allows one to carry over previous schemata results. Theorems describing closure properties and determinacy are then given for serial, concurrent and iterative composition of finishing schemata.