This study investigates a complex task in which rhythmic and discrete components have to be combined in single-joint elbow rotations. While previous studies of similar tasks already reported that the initiation of the discrete movement is constrained to a particular phase window of the ongoing rhythmic movement, interpretations have remained contradictory due to differences in paradigms, oscillation frequencies, and data analysis techniques. The present study aims to clarify these findings and further elucidate the bidirectional nature of the interaction between discrete and rhythmic components. Participants performed single-degree-of-freedom elbow oscillatory movements at five prescribed periods (400, 500, 600, 800, 1,000 ms). They rapidly switched the midpoint of oscillation to a second target after an auditory signal that occurred at a random phase of the oscillation, without stopping the oscillation. Results confirmed that the phase of the discrete movement initiation is highly constrained with respect to the oscillation period. Further, the duration, peak velocity, and the overshoot of the discrete movement varied systematically with the period of the rhythmic movement. Effects of the discrete-onto-rhythmic component were seen in a phase resetting of the oscillation and a systematic acceleration after the discrete movement, which also varied as a function of the oscillation period. These results are interpreted in terms of an inhibitory bidirectional coupling between discrete and rhythmic movement. The interaction between discrete and rhythmic movement elements is discussed in comparison to sequential and gating processes suggested previously.