In this paper, low-complexity multiple-input multiple-output (MIMO) subspace detection schemes are studied, which decompose a channel into multiple decoupled streams to be detected disjointly. Existing schemes require a number of matrix decomposition operations equal to the number of detected streams, which is computationally complex, especially in high-order MIMO systems. We propose two computationally efficient detection algorithms, based on a preprocessing stage that consists of special layer ordering, followed by permutation-robust QR decomposition (QRD) and elementary matrix operations. The algorithms are illustrated in the context of a 4-layer MIMO system, and their complexity is studied. Simulations demonstrate that using the proposed scheme, the QRD overhead is reduced by almost 50% for very high order MIMO, without incurring any performance degradation.