Abstract: A sorted QR decomposition method used in a detection of a multiple input multiple output (MIMO) communication system is provided. First, whether a sorting-stop parameter of a channel transformation matrix of the MIMO communication system is greater than or equal to a sorting-stop threshold is determined. Then, whether energy of elements in a leftmost column within a process area of the channel transformation matrix is completely transferred to a top element in the leftmost column is determined. If the energy of the elements in the leftmost column within the process area is not yet completely transferred to the top element in the leftmost column, a unit process area of a process unit set is expanded.