In this paper, a modified tangential frequency filtering decomposition (MTFFD) preconditioner is proposed. The optimal order of the modification and the optimal relaxation parameter are determined by Fourier analysis. With this choice of the optimal order of modification, the Fourier results show that the condition number of the preconditioned matrix is ${\cal O}(h^{-\frac{2}{3}})$, and the spectrum distribution of the preconditioned matrix can be predicted by the Fourier results. The performance of MTFFD is compared with tangential frequency filtering (TFFD) preconditioner on a variety of large sparse matrices arising from the discretization of PDEs with discontinuous coefficients. The numerical results show that the MTFFD preconditioner is much more efficient than the TFFD preconditioner.