This paper presents a family of rate-one quasi-orthogonal space-time block codes (QO-STBCs) for any number of transmit antennas. Full diversity of the proposed QO-STBCs is achieved via the use of constellation rotation. When the number of transmit antennas is even, these codes are delay "optimal." this property along with the quasi-orthogonality one allows the codes to have low decoding complexity. Besides, by applying lookup tables into the detection methods presented in  and generalizing them, two low-complexity maximum-likelihood (ML) decoders for the proposed QO-STBCs and for other existing QO-STBCs, called PMLD and QMLD, are obtained. Simulation results are provided to verify the bit error rate (BER) performances and complexities of both the proposed QOSTBCs and the proposed decoders.