The “minimal factorization” for rational matrices is considered. As known, in most of the related works, the zero structure and minimal indices of rational matrices are taken into consideration. In addition, the rational matrices are often confined to be proper. The paper shows that the factorization problem with minimal degree, without bothering about the zero structure and minimal indices can be solved in a straightforward way. The main result is that for a complex rational matrix G(s) with McMillan degree n, it can be factorized over the complex field as a product of n rational matrices each of which has McMillan degree 1. The proofs of the presented factorization theorems are derived from a state-space formulation and allow easy numerical construction of the factors.