High-resolution beat-capacity and optical-reflectivity measurements have been conducted on thin free-standing films of n-hexyl-4'-n-pentanoyloxy-biphenyl-4-carboxylate (64COOBC). The data suggest incomplete layer-by-layer liquid-hexatic transitions. The transition in extremely thin films shows a diverging heat-capacity anomaly. The results are compared with those reported in other compounds, and discussed in the context of the theory of two-dimensional melting.