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We present a reassessment of the radial abundance gradients of C, N, O, Ne, S, Cl and Ar in the Milky Way using deep spectra of 33 H II regions gathered from the literature, covering Galactocentric distances from 6 to 17 kpc. The distances of the objects have been revised using Gaia parallaxes. We recalculate the physical conditions and ionic abundances in an homogeneous way using updated atomic data. All the objects have direct determination of the electron temperature, permitting to derive their precise ionic abundances. We analyze and compare different ICF schemes for each element in order to obtain the most confident total abundances. Due to the revised distances, our results do not support previous claims about a possible flattening of the O/H gradient in the inner Galactic disk. We find that the Galactic N/O gradient is rather flat, in contrast to what has been found in other spiral galaxies. The slope of the gradients of some elements is sensitive to the ICF scheme used, especially in the case of Ne. The dispersion around the fit for the gradients of C, N, O, S, Cl and Ar is of the order of the typical uncertainties in the determination of the abundances, implying the absence of significant inhomogeneities in the chemical composition of the ionized gas phase of the ISM. We find flat gradients of log(S/O) and log(Cl/O) and very shallow or flat ones for log(Ne/O) and log(Ar/O), consistent with a lockstep evolution of Ne, S, Cl and Ar with respect to O.