The greater sac-winged bat, Saccopteryx bilineata (Emballonuridae), uses two distinct echolocation call sequences: a 'monotonous' sequence, where bats emit similar to 48 kHz calls at a relatively stable rate, and a frequency-alternating sequence, where bats emit calls at similar to 45 kHz (low-note call) and similar to 48 kHz (high-note call). The frequencies of these low-high-note pairs remain stable within sequences. In Panama, we recorded echolocation calls from S. bilineata with a multi-microphone array at two sites: one a known roosting site, the other a known foraging site. Our results indicate that this species (1) only produces monotonous sequences in non-foraging contexts and, at times, directly after emitting a feeding buzz and (2) produces frequency-alternating sequences when actively foraging. These latter sequences are also characterized by an unusual, offbeat emission rhythm. We found significant positive relationships between (1) call intensity and call duration and (2) call intensity and distance from clutter. However, these relationships were weaker than those reported for bats from other families. We speculate on how call frequency alternation and an offbeat emission rhythm might reflect a novel strategy for prey detection at the edge of complex habitat in this ancient family of bats.