Multiple antennas are used to increase reliability and bit rate for a given bandwidth. For a fixed transmission rate, discrete input alphabets and without channel state information at the transmitter, optimal space-time codes (STCs) achieving both gains (full rate and full diversity) are well known. However, the complexity of maximum likelihood decoding increases exponentially with the number of space and time dimensions of the STC. Previous work reducing the complexity of decoding STCs has focused on the decoding algorithm, because the dimensions of the STC cannot be reduced without losing rate or diversity for uncoded communication. However, for coded communication (assuming the presence of an outer code), the dimensions of the STC may be reduced. We propose a new full-rate and full-diversity suboptimal time-varying space-only code, adding a new dimension to the work on complexity reduction. Full diversity is proved in terms of the outage probability.