This paper presents a method, for determining simultaneously the invariant zeros and the transmission zeros of a large class of linear, time-invariant, invertible, multi-variable systems. The zeros are defined via the concept of minimal order system inverses. These definitions are then used to develop algorithms for determining the positions of the invariant zeros and the transmission zeros. The definitions and algorithms proposed in this paper do not require the systems to be controllable or observable. The zeros are obtained as the eigenvalues of a matrix derived from the system matrices and of order not larger than that of the system. Hence the method is computationally efficient, especially for high-order systems. Three numerical examples are given to illustrate the method.