  Irreducible representations (irreps) of a finite group $G$ are equivalent if
there exists a similarity transformation between them. In this paper, we
describe an explicit algorithm for constructing this transformation between a
pair of equivalent irreps, assuming we are given an algorithm to compute the
matrix elements of these irreps. Along the way, we derive a generalization of
the classical orthogonality relations for matrix elements of irreps of finite
groups. We give an explicit form of such unitary matrices for the important
case of conjugated Young-Yamanouchi representations, when our group $G$ is
symmetric group $S(N)$.
