A catalyst comprising by weight:(a) 10-99.98% of a mordenite, in major part as needles, having a Si/Al atomic ratio of from 5:1 to 100:1, a sodium content lower than 0.2% by weight of the dry mordenite weight, a mesh volume V of elementary mesh from 2.73 to 2.78 nm.sup.3, which adsorbs molecules of a kinetic diameter higher than about 6.6 Angstroms and has a benzene adsorption capacity higher than about 5% by weight,(b) 0-89.98% of a matrix selected from the group formed of alumina, silica, magnesia, natural clays, mixtures of said compounds and alumina-boron oxide combinations,(c) 0.01-15% of at least one group VIII metal, and(d) 0.01-1% of at least one group IV B metal (Ti, Zr, Hf).The catalyst is preferably prepared by introducing the group IV B metal into the matrix, admixing the obtained product with mordenite and then introducing the group VIII metal.The catalyst is used for hydroisomerizing n-paraffins having 4 to 7 carbon atoms with a good conversion rate and a good selectivity, thus obtaining a mixture comprising a high proportion of isoparaffins.