A method has been investigated for the synthesis of memoryless logical networks using a restricted repertoire of functional modules. The method is based on the reduced general solution to a generalized system of Boolean equations (BE) as applied to the decomposition of Boolean functions. The aim of the synthesis is to obtain the most constrained circuit having at most two levels of gating. The constraints take the form of single input variables or constant logic levels applied to the inputs of the first level gate. This is achieved by assembling a set of constraint equations which are then a part of the generalized system of BE. The method is then tested on some synthesis examples of single and multiple output functions in terms of the NAND and (WOS) modules.