This communication presents the results of an investigation of the response of a nonlinear form of the Mathieu equation in the first unstable region. The equation of interest is a Mathieu equation plus a cubic nonlinearity. The response consists of a modulated one‐half subharmonic of the parametric‐excitation frequency. The envelope of the subharmonic is approximately a sinusoid. The magnitude and frequency of this sinusoid are determined by the method of harmonic balance. The results are compared with the results of computer simulation.