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This paper proposes a new invertible two-dimensional map for image encryption in network. The map is a process of stretch-and-fold. Firstly a square image is divide two parts along the diagonal direction. Then they are stretched respectively and joins a array of pixels. Lastly the array is fold over to a new image. The process shuffles the positions of pixels. The map includes two sub maps: the left map and the right map. The security key is used to represent a sequence of number of iterations of the sub maps. Compared with the prevalent map, baker map, the new map has simpler formulation, bigger keys space, faster speed which is fit for image encryption. A symmetric image encryption approach based on the map is developed. The experimental tests are carried out and the results proved the effectiveness of the new approach.