  An algorithm for irreducible decomposition of representations of finite
groups over fields of characteristic zero is described. The algorithm uses the
fact that the decomposition induces a partition of the invariant inner product
into a complete set of mutually orthogonal projectors. By expressing the
projectors through the basis elements of the centralizer ring of the
representation, the problem is reduced to solving systems of quadratic
equations. The current implementation of the algorithm is able to split
representations of dimensions up to hundreds of thousands. Examples of
calculations are given.
