Hochwald et al. introduced unitary space-time codes for quasi-static Rayleigh fading channels which allows for noncoherent decoding when the channel response is not known at the receiver. However, when reliable information on the channel response is available, coherent decoding is preferable for improved performance. Here, we study the relationship between the performance criteria on the diversity and coding advantages provided by unitary space-time codes with noncoherent and coherent decoding. We show that when a unitary space-time code achieves full spatial diversity with noncoherent decoding, full spatial diversity is also guaranteed with coherent decoding.