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A new solar burst emission spectral component has been found showing sub-THz fluxes increasing with frequency, spectrally separated from the well known microwave component. Rapid pulsations are found present in all events observed at the two frequencies of the solar submillimeter-wave telescope: 212 and 405 GHz. They were studied in greater detail for three solar bursts exhibiting the new THz spectral component. The pulse amplitudes are of about 5%-8% of the mean flux throughout the bursts durations, being comparable for both frequencies. Pulsations range from one pulse every few seconds to 8-10 per second. The pulse repetition rates (R) are linearly proportional to the mean burst fluxes (S), following the simple relationship S = kR, suggesting that the pulsations might be the response to discrete flare particle accelerator injections quantized in energy. Although this result is consistent with qualitative trends previously found in the GHz range, the pulse amplitude relative to the mean fluxes at the sub-THz frequencies appear to be nearly ten times smaller than expected from the extrapolation of the trends found in the GHz range. However there are difficulties to reconcile the nearly simultaneous GHz and THz burst emission spectrally separated components, exhibiting rapid pulsations with considerably larger relative intensities in the GHz range.