Unitary space-time modulation (USTM) is a kind of noncoherent space-time block codes. Codes of USTM which have been proposed all use PSK (phase-shift keying) signals. In this paper, we propose three new USTM schemes in which nonconstant-energy signals are used. The first scheme utilizes APSK (amplitude phase-shift keying) signals while the second scheme utilizes APSK signals combined with PSK signals. Codes of both schemes are found by computer searches. In the third scheme, we use the space-time block code to design high-rate USTM. Codes of the proposed schemes all have larger diversity product than codes of USTM using PSK signals.