Abstract: A new class of image scrambling technique named quasi-affine transformation over limited integer grids (QATLIG) is presented, it is based on the idea of building reversible linear transform through mapping integers to integers. Properties and construction of QATLIG are illustrated and its periodicity for digital images is discussed. Experimental results show that for digital image scrambling, QATLIG has a larger period and leads to a better result than Arnold, Fibonacci and other geometric transformations.