The total variation is a useful method for solving noise problems (denoising) because the total variation is very effective for recovering blocky, possibly discontinuous, images from noise data. However, it is not a easy problem to find the true image without noise from the total variation. In this paper a new functional is introduced to find the true image without noise by using the minimizer of the total variation. We prove the convergence of the sequence induced from the modified functional in the iterative scheme, and show that our numerical denoising gives significant improvement over other previous works.