Abstract: A new-style fast wavelet transform, named "rotation angle series fast wavelet transform--RAS-FWT", is put forward in this paper. The restriction on the rotation angle series is also brought forward. Instead of the traditional method based on convolution, RAS-FWT adopts iteration structure that is more easily realized on microprocessors. Digital delay is implemented by "cyclic pointers". So the code will be with higher efficiency and speed. Mallat algorithm established the one-to-one mapping between orthogonal wavelets and N length discrete coefficient series, while RAS-FWT discovers the similar one-to-one mapping between orthogonal wavelets and N/2-1ength discrete angle series. So it has half operations less than FWT. In addition, new techniques based on the "rotation angle series" will inaugurate a brand-new approach for the wavelet construction theory, and will become a new branch of the academic subject.