Staple fibers made from crimped, in particular compression crimped, multicomponent filaments of the matrix/segment type, the cross section of which shows, in addition to the matrix, at least 6 peripheral wedge-shaped or lenticular segments, not completely covered by the matrix, are processed into a web, which is then mechanically bonded, preferably by needling. Subsequently, the fabric is subjected to a shrinkage process, by which its density is increased by more than 30%, the multicomponent fibers being completely or partly split up into their components. The difference in shrinkage between the components should be at least 10%. The liquids used for the shrinkage treatment are in particular organic liquids, such as methylene chloride, as well as other liquids producing a difference in shrinkage of at least 20%. The fabric is then impregnated with a solution of polyurethane on the basis of polyglycols, specifically polytetramethylene glycol, diisocyanates and low-moleclar glycols as chain lengtheners, the jelling temperature of the solution being higher than the room temperature and higher than the temperature of the coagulation bath; the polyurethane is coagulated by cooling and/or treatment with a coagulation bath containing a non-solvent for polyurethane; then the fabric is washed, dried and ground on one or both sides. The suede-like product obtained combines great suppleness with high strength. It is an excellent material for making garments, such as coats, jackets or skirts, offering high wear comfort as well as high breathability.