A new algorithm, which is an extension of [1, algorithm II], is presented to determine the transmission zeros of the system

denoted by

. The algorithm is based on the observation that for nondegenerate

systems, the set of transmission zeros of

are contained in the finite eigenvalues of the closed-loop system matrix

where

is any arbitrary matrix of full rank,

, and

. Some numerical examples of systems of 100th order are included to illustrate the algorithm.