The accuracy of rotation of spindle unit could be defined as the stability of its spindle axis while rotating. The rotation in the rolling bearings causes the disturbing influence, which leads to the oscillation of a rotation axis. The main source of oscillation is the interaction between rolling bodies and rings’ races. The first oscillation source investigated was the out-of-shape imperfection of inner bearing ring. It was shown that it is possible to considerably decrease the radial runout of spindle if we can orient the inner rings in such a manner that oscillations caused by them would mutually compensate each other. Also the outer ring harmonics were explored as the second oscillation source. It was found that it is possible to reduce the runout by making the oscillation antiphased by mutually adjusting position of bearings on assembly stage.