Unitary space-time block codes (STBCs) are attractive because they provide transmit diversity while allowing low complexity detection. Most work with STBCs has been done with non-offset modulations such as QPSK and quadrature amplitude modulation (QAM), but offset modulations such as shaped offset QPSK (SOQPSK) can be attractive in systems employing non-linear power amplifiers. In this paper we explore the application of STBCs to SOQPSK. We show that the offset in SOQPSK complicates the detection of STBC-SOQPSK. Using the Almouti STBC as an example, we present two architectures for detecting unitary STBCs that provide a trade off between decoder complexity and bit error rate performance.