In Genetic Algorithms mutation probability is usually assigned a constant value, therefore all chromosome have the same likelihood of mutation irrespective of their fitness. It is shown in this paper that making mutation a function of fitness produces a more efficient search. This function is such that the least significant bits are more likely to be mutated in high-fitness chromosomes, thus improving their accuracy, whereas low-fitness chromosomes have an increased probability of mutation, enhancing their role in the search. In this way, the chance of disrupting a high-fitness chromosome is decreased and the exploratory role of low-fitness chromosomes is best exploited. The implications of this new mutation scheme are assessed with the aid of numerical examples.