本文主要通过回顾和重新考察狭义相对论下长杆的匀速转动研究，指出伽利略公式在狭义相对论框架下是不自洽的. 利用惯性系下的狭义相对论传递公式，通过连分数和递推关系，导出狭义相对论下匀速转动长杆的转速公式. 这一相对性转动公式中，转动线速度总小于光速的情况，从而伽利略转动公式中的视界问题得到解决. 文中还验证了相对论转动公式的自洽性，并比较了相对论长杆转动和经典转动的横向多普勒频移，其结果可用于检验相对性转动公式.

It is pointed out in the paper that the Galileo formula is not self - consistent in the framework of the special theory of relativity via the investigation of reviewing and reconsidering the pole's uniform rotation within the special relativity. A new formula for the rotate velocity of the pole，which is rotating uniformly，is derived in the special relativistic limits by using the special relativistic delivery formula in the inertial system，and by continued fraction and recurrence relation. In the new relative rotation formula，the rotational linear velocity is always less than the velocity of light. Therefore，the problem of horizon in the Galileo rotation formula can be solved. The self - consistence of the new relative rotation formula is verified，and the comparison of the transverse Doppler shift between the relativistic rotating pole and classical rotating one is made. The result can be used to test the relative rotational formula.