The recursion creation and decomposition of matrix is introduced into singular value decomposition (SVD)

and a signal decomposition way

which is similar to wavelet packet and is called multi-resolution SVD packet

is realized with SVD.The decomposition and reconstruction algorithms of multi-resolution SVD packet are given.Besides

a method in which two-dimensional array is used to store the three-dimensional data of this packet is proposed so that the waste of computer memory can be avoided.The results of examples show that this packet has good ability to detect the faint change of signal

and the accurate position of faint change can be reliably detected

and furthermore

there is no distortion of amplitude and phase in detection result.In addition

this packet can effectively extract the weak fault feature from the complicated signal.In these two cases the processing results of multi-resolution SVD packet is much better than those of wavelet packet.