One of the main concerns in the area of control theory is the ability of a system to remain stable in the presence of unknown perturbations. Consequently, it is important to be able to measure relative stability of systems and thus be able to determine if they are robust and will remain stable when subjected to various perturbations. For single-input single-output feedback systems relative stability in the frequency domain is typically measured in terms of the phase margin and the gain margin. For multivariable systems, however, relative stability in the frequency domain is typically measured at some point in the control loop in terms of the size of the smallest destabilizing perturbation (either multiplicative or additive). The stability margin is a standard technique used to measure relative stability for unstructured perturbations while the Doyle mu function is a common method used to measure relative stability for structured perturbations. The problems with these measurements is that they are based upon the small gain theorem and do not account for any possible phase present in the perturbations. However, the concept of phase for multivariable perturbations was presented in Bar-on (1990), Bar-on and Jonckheere (1990, 1991) where the single-input single-output notions of phase margin and gain margin were generalized to multivariable systems. The purpose of this paper is to develop an explicit lower bound for the amount of phase required for destabilizing perturbations whose size equals the stability margin. It is shown that if both the stability margin and the frequency at which it occurs are known, then one can determine what the required phase is (in terms of Bar-on and Jonckheere) for minimum size unstructured destabilizing multiplicative output perturbations. Thus, the stability margin can be used not only to determine what is the size (or gain) of the smallest destabilizing perturbation, but it can now be used to determine what is the minimum required phase for such a destabilizing perturbation.