The support spacer sector (14) minimizes functional clearances (J) between the end of the blades (3) and the ring (12) of the high-pressure turbine and the assembly clearances of the support spacer sectors (14) on the casing of the high-pressure turbine (1). Each support spacer sector (14) has a tab (20) on the upstream side one end (21) of which is supported on the inside wall (1I) of the casing of the high-pressure turbine (1) thus forming an intimate contact between the attachment parts of this support spacer sector (14) with the corresponding parts of the casing of the high-pressure turbine (1). This invention applies to turbo-machines fitted on an aircraft.