In-place matrix transposition, a standard operation in linear algebra, is a memory bandwidth-bound operation. The theoretical maximum performance of transposition is the memory copy bandwidth. However, due to non-contiguous memory access in the transposition operation, practical performance is usually lower. The ratio of the transposition rate to the memory copy bandwidth is a measure of the transposition algorithm efficiency. This paper demonstrates and discusses an efficient C language implementation of parallel in-place square matrix transposition. For large matrices, it achieves a transposition rate of 49 GB/s (82% efficiency) on Intel Xeon CPUs and 113 GB/s (67% efficiency) on Intel Xeon Phi coprocessors.