The classic algorithm for Sammom’s projection and some new its modifications are examined in details. All the algorithms are oriented to minimize the projection error. Four modifications are developed and examined on the view on the following stand points: projection error – iteration; projection error – computing time; projection error - “magic factor”; projection error – vibration of derivatives; visual analysis of projected data for fixed projection error. The discovered new ways for minimization of the projection error makes a background for the further research in this field.