We show that the frequency of a magnetic tunnel junction (MTJ)-based spin torque oscillator (STO) can be doubled and the first harmonic entirely suppressed by orienting the free and fixed layer magnetizations in an antiparallel (AP) state. The angular dependence of the harmonics allows us to extract the free layer precession angle, which follows a parabolic decrease from a maximum of 20 degrees in the AP state to about 10 degrees at 25 degrees of misalignment. Frequency-doubling provides both a promising way for increasing the frequency of MTJ-STOs and a means for high-rate frequency shift keying using only a small magnetic field.