A general formula, originally to find the scalar partial fraction expansion (PFE) of a (scalar) rational function and the matrix-PFE of a rational transfer matrix, is generalized to find the block-PFE of a right coprime matrix fraction description (MFD) with simple and/or repeated block poles. This formula expresses the block residues explicitly in terms of the coefficient matrices of the numerator and the denominator matrix polynomials, and the left solvents of the denominator matrix polynomial. It is therefore straightforward and easy to apply, as compared with the existing methods.