The invention relates to a catalyst consisting of at least: one matrix comprising at least one oxide which is selected from an amorphous oxide, an oxide with low crystallinity and a mixture of both; at least one solid microporous crystalline material which, in the calcined and anhydrous state, has the molar compositions X.sub.2O.sub.3:nYO.sub.2:mZO.sub.2, in which X is a trivalent element such as, for example, Al, B, Fe, In, Ga, Cr, Y is at least one trivalent element that is different from Ge and Z is Ge, the value (n+m) is at least equal to 5 and can be between 5 and .infin., and the value of n/m is at least equal to 1; and at least one hydrogenating compound, preferably Pt, Pd, It, Ru, Rh, and Re or a combination of same. The invention also relates to the use of said catalyst in a process in order to improve the quality of diesel fractions.