Mita (1977) presented a simple method for the invariant zeros of a linear multivariable system by constructing its maximal unobservable subspace (MUS). However, the results of this method have been restricted to a class of controllable and right invertible systems satisfying the diagonal decoupling condition and described by the triple (A,B,C). Here, a general method based on the theory of decoupling extends Mita's results for all classes of systems described by the 4-tuples (A, B, C, E) with no special requirements. The MUS of all classes of such systems is simply constructed and its order is given in terms of the system order n and the infinite zeros or the minimal observability indices of the system. In addition, the invariant zeros and zero directions are found from the eigenvalues and eigenvectors of a reduced-order matrix having the dimension of the MUS obtained directly from the state-space parameters. Algorithms are presented for the invariant zeros and zero directions of invertible decouplable (or non-decouplable) systems S(A, B, C, E) and all classes of invertible and non-invertible systems S(A, B, C, E). Numerical examples demonstrate the generality and feasibility of the proposed method.