The invention relates to a new hydrocarbon hydroconversion catalyst, which is a mixture of an amorphous matrix, a zeolite and at least one metal of Group VIII and optionally of Group VI, the zeolite having a SiO.sub.2 /Al.sub.2 O.sub.3 molar ratio of about between 8 and 70, a sodium content of less than 0.15% by weight, a unit mesh parameter a.sub..degree. of between 24.55 and 24.24.times.10.sup.-10 m, a sodium ion recovery capacity C.sub.Na, expressed in grams of sodium per 100 grams of modified zeolite, greater than 0.85, a specific surface area greater than 400 m.sup.2 g.sup.-1, a water vapor adsorption capacity at 25.degree. C. (with a P/Po ratio of 0.10) greater than 6% by weight, a pore distribution between 1 and 20% of the pore volume contained essentially in pores of diameters between 20 and 80.times.10.sup.-10m, the remaining pore volume being contained essentially in pores of diameters less than 20.times.10.sup.-10 m, the matrix being characterized by the following textural properties:S.gtoreq.100 m.sup.2.g.sup.-1Vpt.gtoreq.0.4 cm.sup.3.g.sup.-1V.sub.75 .gtoreq.0.25 cm.sup.3.g.sup.-1V.sub.75 /Vpt.gtoreq.0.5.