This paper considers maximum-likelihood (ML) detection of orthogonal space-time block coded OFDM (OSTBC-OFDM) systems without channel state information. Our previous work has shown an interesting identifiability result, that the whole time-domain channel can be uniquely identified by only having one subchannel to transmit pilots. However, this identifiability is in a probability-one sense, under some mild assumptions on the channel statistics. In this paper we establish a "perfect" channel identifiability (PCI) condition under which the channel is always uniquely identifiable. It is shown that PCI can be achieved by judiciously applying the so-called non-intersecting subspace OSTBCs. The resultant PCI achieving scheme has its number of pilots larger than that used in the previous probability-one identifiability achieving scheme, but smaller than that required in conventional pilot-aided channel estimation. Simulation results are presented to show that the proposed scheme can provide a better performance than the other schemes.