Breakthrough of single-quantum coherence is shown to occur after application of a double-quantum filter with the conventional four-step phase-cycling scheme. This single-quantum breakthrough is due to the intersequence stimulated echo which has been generated by the radiofrequency pulses in the preceding pulse sequence and appears at the same time as the double-quantum coherence signal in the current pulse sequence. Moreover, the phase of the intersequence stimulated echo is the same as the phase of the double-quantum coherence signal; i.e., the phase of the intersequence stimulated echo is twice the phase change of the radiofrequency pulses in the creation period when their phase is rotated in accordance with the conventional four-step phase-cycling scheme. Consequently, the intersequence stimulated echo passes through the double-quantum filtration in the conventional four-step phase-cycling scheme and gradient pulses. A new phase-cycling scheme which can filter out the single-quantum breakthrough signal is proposed here and its effectiveness is verified experimentally and by computer simulations.