Robustness of the optimality of linear quadratic (LQ) optimal regulators is studied. It is shown that under a mild assumption, optimality of LQ regulators is preserved under small perturbations on bothFandGmatrices. This is made possible by allowing modifications on both weighting parametersQandR, and it also extends the existing results where perturbations onFonly are allowed. It is also observed that this modification leads to a possible change in gain margin. A numerical example is discussed in detail to illustrate the results.