ISAF (icosahedral symmetry-adapted functions) algorithm is the new high-resolution algorithm of icosahedral macromolecules. But its running speed is very slow because of the time-consuming operations of mapping sampling points into 3D space. In this paper, a new sampling method is proposed to improve the running speed of this stage. First of all, the angle corresponding to one pixel arc in the maximum Fourier ring is taken as the sampling angle and the same angle sampling is applied in every rings. After that, the sampling points in radius one ring are mapped into 3D space. Finally, the 3D spatial positions of radial sampling points in other rings can be deduced quickly according to the rotate angle invariability of radial sampling points. The HBV (Hepatitis B Virus) Cryo-electron microscopy images are used for validating this strategy. At the high resolution of 6.64 angstrom, the local speedup in the stage of mapping sampling points reaches to 50, and the overall speedup can be improved in an order of magnitude. The overall speedup increases with the increasement number of EM images and the improvement of target resolution.