This paper discusses a near-optimal detection algorithm for 2times2 multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems operating on ultrawideband (UWB) channels. The reported affine restoration (AR) algorithm exploits the independence among the elements of the channel matrix and performs a parallel detection process at all receive antennas. For performance approaching that of maximum likelihood (ML) detection, but with lower complexity, the channel state information (CSI) at the receiver is utilized to restore the transmitted vector without channel matrix inversion or decomposition. We create a subset of the ML search space so as to reduce the computational complexity with minimal compromise on performance. We also discuss a modification in the proposed algorithm to further reduce the detection complexity. The proposed algorithm achieves near-optimal performance as demonstrated through simulations.