Recently, numerous Finite Impulse Response (FIR) system identification methods based on High Order Statistics (HOS) have been proposed in the literature. These methods can be classified into three categories: closed-form solutions, linear algebra solutions and nonlinear optimization based solutions. Because of their simplicity, closed-form and linear algebra solutions are the ones most used in practice. In this paper, we propose a new explicit solution based on fourth-order cumulants. Compared to existing closed-form solutions, the proposed solution uses more statistics and compared to linear algebra solutions it needs less arithmetical operations. This solution is based on a Cholesky type decomposition of a positive definite Hermitian matrix made up of fourth-order cumulants. An efficient algorithm is given to estimate this matrix. Then, the proposed FIR system identification method is applied to estimate the impulse response (i.r.) coefficients of a radio communication channel in order to “open the eyes” of the channel by minimizing the Mean-Square Error (MSE) criterion. The performance of the proposed method is illustrated by some simulation results.