Walsh functions are widely used in many areas such as signal and image processing, digital communication etc. Walsh function system is orthogonal and completed. Among many methods to generate Walsh functions, Swick’s copy theory is famous. This method takes Walsh function’s order numbers as the copy information and can generate an arbitrary function given certain order number, which in fact is the vector processing method and is not applicable for such 2D signal processing applications as fast transforms. Walsh function system can be expressed by Walsh matrix W_k. In this paper, row copy and block copy methods are put forward based on W_k. Copy operators are designed based on symmetries and a new ordering is discovered (named Walsh-Like ordering). After the iterative formulas of 6 ordering Walsh matrices are deduced by Kronecker product, the computer images of these matrices are illustrated. It is proved that the proposed method is more advanced than the former. The later can achieve higher performance and is applicable to the fast transforms designing. The fourth symmetric ordering of Walsh function system is discovered (Walsh-Like ordering), and the conjecture that the new ordering is likely to be the reverse form of Walsh ordering is made by analyzing and comparing with these images.