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The total variation (TV) model is one kind of second-order partial differential equation (PDE) for image noise removal. However, the second-order PDEs suffer from the so-called staircase effect. Proposed is a modified TV (MTV) model, which is staircase-free by minimising the variation of the image along the direction tangential to the isophotes of the original image. Its effectiveness in preserving edges, avoiding staircases and removing noises is shown by experiment and comparison.