Abstract A sufficient condition is given for the existence of a static output feedback which shifts the poles of a linear time-invariant multivariable control system into a specified complex domain Cg- The proof of this result also shows how existing output feedback pole assignment methods may be applied to the Cg-stabilization problem; for example it is shown that the result of Li (1972) is a special case of the results of the present paper. In addition some previously published sufficient conditions for arbitrary pole assignment by output feedback are investigated in order to set out in a more concise form than hitherto the circumstances in which these conditions apply.