A new and fast algorithm is presented for calculating the Padé-Hermite form for a vector of power series. This algorithm works both when the vector of power series is normal (that is, the coefficient matrix corresponding to the A_i(z)s is nonsingular) and in nonnormal cases. The complexity for the normal case is the same as that of algorithms developed before. The strong point of this paper is that the algorithm works for the nonnormal case. This work is a conference paper and as such does not give a thorough exposition of the algorithm. Also, a lack of examples makes this paper difficult to read.