This paper considers the problem of parametrizing (through the minimum number of parameters) the minimum-time output deadbeat controller (MTODC) for a given linear multivariable output-controllable system S(A, B, C, E) having n states, m inputs, p outputs and a transfer function matrixH(z)of full rankr. The main result is a new compact linear parametric form for a class of MTODC that zeros the outputs of the system S in the minimum number of control iterations μ(1), where μ(1), i = 1, 2,..., r (assumed to be decreasingly ordered) are equal lo the negatives of the right factorization indices at infinity ofH(z). The developed parametric class is a linear function in