Recently an algebraic construction of (nt × Q) space-frequency (SF) codes over finite field ℱq was proposed for use in MIMO-OFDM systems, where nt is the number of transmit antenna and Q = qnt - 1 is the number of subcarriers employed in the code. One inconvenience arising from that construction is that the number of subcarriers Q can sometimes be insufficient for constructing codes of large minimum column distance. To completely eliminate this disadvantage, an alternative construction of SF codes with Q = qm - 1 is provided in this paper, whenever m is a multiple of nt. Lower bounds on the minimum rank and column distances of the proposed construction are also given. Simulation results show that the newly constructed codes provide a significant improvement in SNR compared to other SF codes available in the literature.