Generation of one of the auxiliary inputs in model reference adaptive control systems requires a positive definite quadratic function of

system variables for an

th order system. To generate such a function can require as many as

signal multiplications. In this paper, it is shown how this input can be replaced by one that is much simpler to generate and reduces the number of signal multiplications required to one. The property of global asymptotic stability of the closed-loop adaptive system is preserved with the simpler auxiliary input.