The invention relates to a device forming a foil air bearing, comprising a cylindrical sleeve (10) extending along a longitudinal direction, and having an inner surface (11) which defines a central bore, characterized in that it further comprises: at least one longitudinal notch (40, 50, 60) formed in said cylindrical sleeve and opening radially into said central bore; a first peripheral inner lining, called the bump lining, comprising at least one metal foil equipped with radial projections, called the bump foil (22, 23, 24), each bump foil having, at each end, a radial tongue, called the radial bump tongue (22a, 22b, 23a, 23b, 24a, 24b), housed freely in a longitudinal notch (40, 50, 60); a second peripheral inner lining, called the top lining, comprising at least one metal foil, called the top foil (32, 33, 34), each top foil having, at each end, a radial tongue, called the radial top tongue (32a, 32b, 33a, 33b, 34a, 34b), housed freely in a longitudinal notch (40, 50, 60).