We present values of temperature and spectral index of the Galactic diffuse radiation measured at 600 and 820 MHz along a 24h right ascension circle at declination δ = + 42°. They have been obtained from a subset of absolute measurements of the sky temperature made with TRIS, an experiment devoted to the measurement of the CMB temperature at decimetric wavelengths with an angular resolution of about 20°. Our analysis confirms the preexisting picture of the Galactic diffuse emission at decimetric wavelength and improves the accuracy of the measurable quantities. In particular, the signal coming from the halo has a spectral index in the range 2.9-3.1 above 600 MHz, depending on the sky position. In the disk, at TRIS angular resolution, the free-free emission accounts for the 11% of the overall signal at 600 MHz and 21% at 1420 MHz. The polarized component of the Galactic emission, evaluated from the survey by Brouw and Spoelstra, affects the observations at TRIS angular resolution by less than 3% at 820 MHz and less than 2% at 600 MHz. Within the uncertainties, our determination of the Galactic spectral index is practically unaffected by the correction for polarization. Since the overall error budget of the sky temperatures measured by TRIS at 600 MHz, that is, 66 (systematic) + 18 (statistical) mK, is definitely smaller than those reported in previous measurements at the same frequency, our data have been used to discuss the zero levels of the sky maps at 150, 408, 820, and 1420 MHz in literature. Concerning the 408 MHz survey, limiting our attention to the patch of sky corresponding to the region observed by TRIS, we suggest a correction of the base level of +3.9 +/- 0.6 K.