The propagation of highly synchronous firings across neuronal networks, called the synfire chain, has been actively studied both theoretically and experimentally. The temporal accuracy and remarkable stability of the propagation have been repeatedly examined in previous studies. However, for such a mode of signal transduction to play a major role in processing information in the brain, the propagation should also be controlled dynamically and flexibly. Here, we show that inhibitory but not excitatory input can bidirectionally modulate the propagation, i.e., enhance or suppress the synchronous firings depending on the timing of the input. Our simulations based on the Hodgkin-Huxley neuron model demonstrate this bidirectional modulation and suggest that it should be achieved with any biologically inspired modeling. Our finding may help describe a concrete scenario of how multiple synfire chains lying in a neuronal network are appropriately controlled to perform significant information processing.