Abstract: The conventional 2D matrix transform represented by 2D Arnold transform and 2D Fibonacci-Q transform is applied widely in the security of image information, because of its easily selected scrambling variables and its abilities in enduring erasing, cropping and compression attacks. However, this scrambling method can only be used to scramble square image. For any rectangle image with its width not equal to its height, it needs to be expanded into square image or divided into several square images before using 2D matrix transform to scramble it, which adds the extra space or increases the computation cost. To address this problem, this study proposes two kinds of 2D matrix transforms called 2D triangular mappings and also gives their corresponding inverse transforms. The proposed mappings can be used to scramble or recover rectangle image directly and their iterative cost is low. The cost to scramble or recover image for one time is only the numbers of pixels and our proposed mappings need not to compute the iterative period in advance. Experiments show the proposed mappings validity in scrambling rectangle image, low cost in scrambling and recovering rectangle image and robustness in enduring erasing, cropping and compressing attacks.