Spatial-division multiplexing (SDM) provides very high spectral efficiency in multiple-input multiple-output (MIMO) systems. A well-known SDM-MIMO wireless system is vertical Bell Labs layered space-time (V-BLAST) which exhibits a good tradeoff between performance and complexity. Although maximum likelihood detection (MLD) has the optimal performance, its complexity is too high to practice such that some alternatives have been studied. The ordered successive interference cancellation (OSIC) algorithm was proposed for the advantage of high feasibility, however, there is a significant performance gap between MLD and OSIC. Here, we propose a modified layered OSIC algorithm to improve symbol detection in ill-conditioned layers with lower complexity compared to exhaustive search methods. To reduce the number of calculating matrix inversion for optimal ordering, we introduce a modified parallel interference cancellation method with precancellation and postcancellation to replace part of successive interference cancellation, based on evaluating the post-detection signal to noise ratio for each layer. Complexity analysis shows that the proposed algorithm saves about 65% operation of matrix inversion compared to a near-optimal improved layered OSIC algorithm while maintaining the similar bit error rate performance as shown in numerical results.