It is known that by employing space-time-frequency codes (STFCs) to frequency selective MIMO-OFDM systems, all the three diversity viz spatial, temporal and multipath can be exploited. There exists space-time-frequency block codes (STFBCs) designed using orthogonal designs with constellation precoder to get full diversity (Z. Liu, Y. Xin and G. Giannakis IEEE Trans. Signal Processing, Oct. 2002). Since orthogonal designs of rate one exists only for two transmit antennas, for more than two transmit antennas STFBCs of rate-one and full-diversity cannot be constructed using orthogonal designs. This paper presents a STFBC scheme of rate one for four transmit antennas designed using quasi-orthogonal designs along with coordinate interleaved orthogonal designs (Zafar Ali Khan and B. Sundar Rajan Proc: ISIT 2002). Conditions on the signal sets that give full-diversity are identified. Simulation results are presented to show the superiority of our codes over the existing ones