The most accurate realization of a quasi inertial reference frame, the International Celestial Reference Frame (ICRF), is made of 212 defining extragalactic radio sources whose coordinates are determined using VLBI observations. Recent studies demonstrated however that using other sets of sources could improve the frame stability. This study examines a simple radio source selection scheme to define celestial reference frame axes more stable than the ones as currently defined by the ICRF. After having derived source coordinate time series from 26 years of VLBI observations, we select the most suitable sources on the basis of their positional variability (rms and slope), and observational history. We determine the axis stability of the frame defined by the selection, as well as its suitability for global geodetic VLBI analyses, i.e., determination of Earth orientation parameters and source and station coordinates.