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The supermassive black hole (SMBH) with 4 millions solar mass inside theradio-source Sgr A* in our Galactic center is the nearest SMBH. Once the Sstars with shorter period are observed, the relativistic precessions especiallythe Lense-Thirring one can be measured by astronomical observations at 10micro-arcsecond ($\mu$as) level in future. An interesting but so far noattended problem is that the SMBH has not only spin but also spin precessionlike the other objects in the universe. In this paper, we study the effect ofsuch spin precession on the orbital precessions of orbiting stars. Our resultsshow that the spin precession can produce a periodic oscillation on theprecession of the star's orbital plane, but no obvious effect on the periapseshift. For stars with $O(0.1)$yr period, such visible oscillations occur whilethe SMBH's spin-precession period is about from few tens of years to hundredsof years. And the period of oscillation is the same with the one of the spinprecession. In principle, this oscillating orbital plane's precession can beobserved and then the spin and spin precession of the nearest supermassiveblack hole can be determined.

Possibility of Measuring spin precession of the nearest supermassive black hole by S stars