The purpose of this paper is to propose a framework for constructing correct parallel processing programs based on Equivalent Transformation Framework (ETF). ETF regards computation as In the framework, a problem-s domain knowledge and a query are described in definite clauses, and computation is regarded as transformation of the definite clauses. Its meaning is defined by a model of the set of definite clauses, and the transformation rules generated must preserve meaning. We have proposed a parallel processing method based on “specialization", a part of operation in the transformations, which resembles substitution in logic programming. The method requires “Memo-tree", a history of specialization to maintain correctness. In this paper we proposes the new method for the specialization-base parallel processing without Memo-tree.