Based on the analytical results of wavelet transform from data of the atmospheric turbulence experiments on a near-ground surface, it is found that the high-frequency components of the turbulent velocity fluctuation make no contribution to the energy cascade, which is governed only by the low-frequency components in nature. The power density spectrum of turbulence velocity shows that if the timescale of wavelet transform varies as 2j(j = 1,2,…), the eddy will cascade in a manner of (2j-1- 1). The results of wavelet transform using different basis function of wavelet are consistent with each other. In order to characterize the new pattern of turbulence cascade, synchrocascade pattern, a so-called Cantor complementary set $overline {C}$ is constructed from Cantor middle third set C. The set $overline {C}$ is a geometric representation of the hierarchical structures and multiscale properties of turbulence. Using transfer probability as a mathematical tool, we strictly derived the turbulence scaling law for high-order moment from such a geometric pattern. It is easy to determine all parameters contained in the scaling law using intuitive geometric relationship. The synchrocascade pattern, which is very different from Richardson-Kolmogorov's models <Richardson, 1922; Kolmogorov, 1941>, shows that the energy of turbulence is fractal, intermittent, and nonuniform. At the same time, some predictions can be made from the new cascade pattern, especially from the fact that the measure of Cantor complementary set $overline {C}$ is equal to 1, which means that the whole physical space of the fluid will be gradually filled with smaller and smaller eddies, as the scale gradually approaches Kolmogorov dissipative scale η. It agrees quite well with the actual picture observed in practical turbulence.