Let be the adjacency characteristic polynomial of a digraph . In the paper Deng and Kelmans (2013) the so-called -transformation of a simple digraph was considered, where , and the formulas of were obtained for every -regular digraph in terms of , the number of vertices of , and . In this paper we define the so-called -transformation of a simple digraph , where . This notion generalizes the previous notion of the -transformation , namely, if and only if . We extend our previous results on to the -transformation by obtaining the formulas of , where and , for every simple -regular digraph in terms of , the number of vertices of , and . We also use -transformations to describe various constructions providing infinitely many examples of adjacency cospectral non-isomorphic digraphs.