A new, nonassertional approach to proving multiprocess program correctness is described by proving the correctness of a new algorithm to solve the mutual exclusion problem. The algorithm is an improved version of the bakery algorithm. It is specified and proved correct without being decomposed into indivisible, atomic operations. This allows two different implementations for a conventional, nondistributed system. Moreover, the approach provides a sufficiently general specification of the algorithm to allow nontrivial implementations for a distributed system as well.