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The paper describes a method of program development which guarantees correctness. Our programs consist of an operational part, called instruction, and a specification. Both these parts are subject to the development and the refinement process. The specification consists of a pre-and postcondition called global specification and a set of assertions called local specification. A specified program is called correct if: 1) the operational part is totally correct w.r.t. the pre-and postcondition, 2) the precondition guarantees nonabortion, 3) local assertions are adequate for the proof of 1) and 2). The requirement of nonabortion leads to the use of a three-valued predicate calculus. We use McCarthy's calculus in that place. The paper contains a description of an experimental programming language PROMET-1 designed for our style of programming. The method is illustrated by the derivation of a bubblesort procedure.