Supersonic air inlet of an aircraft propulsion assembly , said aircraft propulsion assembly extending longitudinally along an axis (X) oriented from upstream to downstream and comprising a turbine engine configured to enable propulsion of the aircraft at supersonic speeds from the acceleration of a subsonic air flow (F) circulating from upstream to downstream in the turbine engine , said supersonic air inlet comprising: • a pipe with a longitudinal axis (X) comprising an inner wall configured to guide the air flow (F) into the turbine engine and an outer wall connected upstream by an air inlet lip and together delimiting an annular cavity , • a speed reducer fixedly mounted inside the pipe along the longitudinal axis (X) and comprising a conical external wall with an upstream tapered edge so as to generate a shock wave reducing the supersonic speed of the air flow (F) entering the pipe to a subsonic speed, and • at least one support arm connecting the speed reducer to the pipe , said support arm comprising an upstream external wall and a downstream external wall together delimiting a cavity extending from the inner wall of the pipe to the speed reducer along an axis (Z) directed inwards, • a supersonic air inlet characterized in that it comprises at least one de-icing device comprising: • an internal wall mounted in the cavity of the support arm opposite the upstream external wall so as to delimit together a calibrated de-icing space (V), • at least one member for supplying the de-icing space (V) with a de-icing air flow (F D ), and • at least one member for discharging the de-icing air flow (F D ) from the de-icing space (V). • a pipe with a longitudinal axis (X) comprising an inner wall configured to guide the air flow (F) into the turbine engine and an outer wall connected upstream by an air inlet lip and together delimiting an annular cavity , • a speed reducer fixedly mounted inside the pipe along the longitudinal axis (X) and comprising a conical external wall with an upstream tapered edge so as to generate a shock wave reducing the supersonic speed of the air flow (F) entering the pipe to a subsonic speed, and • at least one support arm connecting the speed reducer to the pipe , said support arm comprising an upstream external wall and a downstream external wall together delimiting a cavity extending from the inner wall of the pipe to the speed reducer along an axis (Z) directed inwards, • a supersonic air inlet characterized in that it comprises at least one de-icing device comprising: • an internal wall mounted in the cavity of the support arm opposite the upstream external wall so as to delimit together a calibrated de-icing space (V), • at least one member for supplying the de-icing space (V) with a de-icing air flow (F D ), and • at least one member for discharging the de-icing air flow (F D ) from the de-icing space (V). • an internal wall mounted in the cavity of the support arm opposite the upstream external wall so as to delimit together a calibrated de-icing space (V), • at least one member for supplying the de-icing space (V) with a de-icing air flow (F D ), and • at least one member for discharging the de-icing air flow (F D ) from the de-icing space (V). <EOS>