In this paper, we revisit the problem of the determination of the frequency of occurrence of galactic nova outbursts which involve an oxygen-neon (ONe) white dwarf. The improvement with respect to previous work on the subject derives from the fact that we use the results that our evolutionary calculations provide for the final mass and for the chemical profiles of intermediate-to-massive primary components of close binary systems. In particular, the final evolutionary stages, such as the carbon burning phase, have been carefully followed for the whole range of masses of interest. The chemical profiles obtained with our evolutionary code are of interest in determining the chemical composition of the ejecta after being processed through the thermonuclear runaway, although such other factors as the efficiency of the mixing between the accreted material and that of the underlying white dwarf must also be considered. In our calculations of the frequency of occurrence of nova outbursts involving an ONe white dwarf, we also take into account the observational selection effects introduced by the different recurrence times of the outbursts and by the spatial distribution of novae. In spite of the very different evolutionary sequences, we find that approximately 1/3 of the observed nova outbursts should involve an oxygen-neon white dwarf, in agreement with previous theoretical estimates.