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The blind maximum-likelihood (ML) detection of a general space-time block code (STBC) is considered a challenging implementation problem. Recent work has revealed that for the orthogonal STBCs (OSTBCs), their special code structures can be exploited to formulate highly effective blind ML-based algorithms. Attracted by this realization merit, this paper investigates the blind ML identifiability of OSTBCs, with an emphasis on the binary PSK (BPSK) and quaternary PSK (QPSK) constellations. We find a class of OSTBCs, called the nonrotatable OSTBCs, that can be uniquely identified up to a sign (UIUTS) almost surely under a few mild assumptions. For example, for an independently distributed Rayleigh channel with any number of receiver antennas, a nonrotatable OSTBC can be UIUTS with probability 1. While this identifiability looks appealing already, we further examine a subclass of nonrotatable OSTBCs, called the nonintersecting subspace (NIS) OSTBCs. We prove that NIS-OSTBCs are UIUTS for any nonzero channel. However, NIS-OSTBCs are not available in the existing literature. To fill this gap, we devise a code construction procedure that can convert any (BPSK or QPSK) OSTBC to an NIS-OSTBC.