Sloping roof space insulation installation with a main portion comprising an upper face (12a), a lower face (12b) which is supported on a roof space floor, and a tapered portion (12c) which is arranged at an end of the main portion, and is in contact with the said floor and with a lower roof surface in the vicinity of a lower edge of the roof, comprising a mat (12) of loose insulation selected from amongst: stone wool, glass wool and cellulose, and a unit permeable to air, provided with regularly distributed openings (11d), arranged on the surface of the tapered portion (12c) and retaining the loose insulation which forms part of the said tapered portion (12c).