The definition of the DMP inverse of a square matrix with complex elements is extended to rectangular matrices by showing that for any A and W, m by n and n by m, respectively, there exists a unique matrix X, such that $XAX = X$, $XA = WA_{d,w}WA$ and $(WA)^{k+1}X = (WA)^{k+1}A^\dagger$, where $A_{d,w}$ denotes the W-weighted Drazin inverse of A and k = Ind(AW), the index of AW.