We study decentralized designing of the graph shift operators to implement linear transformations between graph signals. Since this operator captures the local structure of the graph, the proposed method of this paper gives rise to decentralized linear network operators. Unfortunately, existing decentralized approaches either consider some special instances of linear transformations or confine themselves to some known graph shift operators reduced family of the designing linear transformations task. To remedy these limitations, this paper develops a framework for computing a wide class of linear transformations in a decentralized fashion by relying on the notion of graph shift operator. To this end, a set of successive graph shift operators is implemented to compute linear transformations in a small number of iterations (as fast as possible).