An improved program-synthesizing algorithm based on the algorithm proposed by Waldinger and Lee in 1969 is given. In the old algorithm, the program-synthesizing problem is translated into a theorem-proving problem, and a program is obtained by analyzing a proof. For the improved algorithm, the analysis is not necessary, and a program is obtained as soon as the proof is completed. This is achieved by using a modified variable tracing mechanism invented by Green in 1969. The correctness of the improved algorithm is also proved; i.e. the program thus obtained always satisfies the specification.