Maximum-likelihood (ML) detection in a multi-antenna system can be cast as a problem of closest point search in a finite lattice, which can then be efficiently solved by a sphere decoder. Although the state-of-art sphere decoding algorithms proposed by M.G. Damen et al. (see IEEE Trans. Inf. Theory, vol.49, no.10, 2003) have considered the finiteness of the lattice, many points outside the finite lattice are still tested, resulting in much unnecessary computation. We address this problem by incorporating true lattice-boundary-awareness, such that testing on any point outside the finite lattice is completely avoided. This new lattice-boundary-aware sphere decoder offers two important advantages: (i) compared to the sphere decoder proposed by Damen et al., it achieves up to 32% reduction in the number of multiplications and up to 39% in the number of additions; (ii) the complexity reduction tends to increase as SNR decreases. The proposed approach can thus significantly relax the requirements on hardware implementation of the sphere decoder.