One of the most basic tasks required in solving finite fixed-time linear- quadratic-regulator problems is the specification of a terminal penalty matrix. In theory, a matrix (frequently, a diagonal matrix) whose elements are large in an engineering sense is simply selected. However, the resulting control-gain histories often exhibit fluctuations of several orders of magnitude near the end of the control interval. Theoretically, this is not a problem because the states are close to zero when the fluctuations occur. Compuationally, however, it is difficult to simulate the closed-loop system response when the control gains are varying rapidly. In an effort to overcome this problem, a simple algorithm for selecting the terminal penalty weighting matrix is presented in this note; the algorithm minimizes the large fluctuations in the terminal values of the control gains while satisfying the terminal- state boundary conditions.