In this paper, a method to construct an integer version of the linear transform is presented so that the integers of input data can be mapped to integers. Based on the introduction of three kinds of basic integer reversible transform, by means of matrix decomposition, the sufficient and essential condition that a linear transform can be rebuilt into integer version and its construction method are proposed. The transform is reversible, so it is suitable to the lossless data processing such as the lossless digital audio or image compressions.