Here, a new spectrum sensing method, called mean-to-square extreme eigenvalue (MSEE), is proposed. Considering a multiple antenna communication system, the proposal is drawn from the arithmetic-to-geometric mean (AGM) algorithm using only the smallest and the largest eigenvalues of the covariance matrix of the received signal. The aim of MSEE is to avoid the heavy computational costs of AGM method. First, based on the random matrix theory, a theoretical development to set the threshold of the proposal is provided. Then, the validity of the expression is verified by simulations. Finally, simulation results show an interesting performance of MSEE compared with several spectrum sensing methods in the literature.