The four optimum rotation angles for a polarimeter consisting of a quarter-wave plate in conjunction with a linear polarizer are found. This is done by using the determinant and condition numbers of the system measurement matrix as objective functions in a minimization procedure. The four angles so found result in the polarimeter's estimate of the incident Stokes vector to have a minimum sensitivity with respect to fluctuations in the detected flux and errors in the angular position of the optical components constituting the polarimeter. Four optimal angles are presented. These four angles also retain a simplicity of form for the measurement matrix.