For diagonally perturbed linear time-invariant multivariable feedback systems, the problem of finding an improved characterisation of the stability margin is examined. A readily computable lower bound for diagonally perturbed systems is developed using Perron-Frobenius non-negative matrix results. The present theory improves upon the existing singular-value stability-margin theory, providing a simple constructive method for determining previously unspecified norm weighting parameters (i.e. scaling factors) so as to minimise the conservativeness of stability-margin bounds.