New method for the synthesis of algorithm formulae based on the concept of algorithm algebra is presented. The concept of algorithm algebra there is shown in papers [1-4]. The synthesis is performed in two stages. First, all sequences are formulated, which is followed by the bonding the sequences by conditions. This operation is termed by elimination. If the algorithm contains a cyclic operations, then each cyclic operation is considered as a complex one, over which the synthesis of sequences and eliminations are successively performed. Additionally, the algorithm algebra tools for transformation and minimization of algorithms are illustrated by a simple but instructive example.