We discuss a novel design of a self-starting regenerative divider that permits division by 3, 4, 5, 6 ... instead of the usual 2. This is accomplished by having the loop oscillate simultaneously at two harmonically related conjugate frequencies, e.g., at nu/4 and 3nu/4. A prototype of the divide-by-four circuit has been constructed for an input frequency of 400 MHz. This divider exhibits very low phase noise, Fourier frequency (1 kHz) = -162 dBc/Hz and Fourier frequency (100 kHz) = -170 dBc/Hz, which is approximately 9 dB lower than that of its constituent parts. Simple modifications of the feedback loop of this circuit enabled it to divide by 3, 5, and 8. Operation at higher division ratios appears feasible under certain conditions.