Jacketing boot to the housing of a turbine engine and method of carrying out the coating

This coating is characterized in that it is placed between the free ends of the blades (3) and the housing (1) of a compressor or a turbine of a turbomachine, said coating being formed of a support (7) and the fiber bundle (5) to be secured to the periphery of the housing (1), and method for the implementation of the coating, characterized in that: a) placing bundles fibers (5) in a support (7) so that the free ends (10) of the fiber bundles (5) are directed radially inwardly b) securing the bundles of fibers (5) in the support (7), c) fixing the support (7) in the housing (1).