Time series of the coordinates of the ICRF radio sources were analyzed. It was shown that part of radio sources, including even the so-called “defining” sources, show a the significant apparent motion. Corrections for their a priori coordinates are time functions. The celestial reference frame stability is provided by the no-net-rotation condition applied to the selected subset of sources, which leads in our case to a rotation of the frame axes with time. Parameters of this rotation were calculated for different subsets of sources.To improve stability of the celestial reference frame new methods of selection of the extragalactic radio sources were suggested. The first one was called “cosmological” and the second one “kinematical”. It was shown that a selected subset of the ICRF sources, according to cosmological criteria, determines the most stable coordinate system during next decade.