This paper is concerned with the investigation of a 2-parametric linear stationary iterative method, called Modified Extrapolated Jacobi method, for solving the linear systems $Ax=b$, where $A$ is nonsingular consistently ordered 2-cyclic matrix. We give sufficient and necessary conditions for strong convergence of the MEJ method and we determine the optimum extrapolation parameters and the optimum spectral radius of it, in the case where all the eigenvalues of the block Jacobi iteration matrix associated with $A$ are real. In the last section, we compare the MEJ with other known methods.