with fig3 the smoothing brush 3 comprises a body with a cylindrical grip 30 positioned in the extension of a head 31 for diffusing the steam said head 31 having a flat front surface 31 a equipped with a steam emission hole 32 in the shape of an oblong slit more particularly according to the invention and in accordance with fig4 to 8 the smoothing brush 3 comprises a steam flow acceleration device 4 by generating a puff of air to increase the steam flow rate at the outlet of the smoothing brush 3 this steam flow acceleration device 4 has a fan 40 controlled by a button 5 on the handle 30 said fan 40 blowing through a hose 41 that passes through the body of the smoothing brush 3 and comprises an air intake 41 a positioned on the exterior of the smoothing brush 3 as well as an air ejection nozzle 43 opening into the smoothing head 3 as an example the fan 40 consists of an axial fan that traditionally has a propeller powered by an electric motor integrated into the propeller boss that delivers 1 watt of power via cables not shown on the figures which extend along the flexible conduit 2 to the base 1 in accordance with fig6 and 7 the fan 40 is preferably disposed in a housing 42 that extends outside the body of the smoothing brush 3 at the end of the hose 41 with the air intake 41 a the hose 41 has a convergent shape from this end of the hose 41 with the air intake 41 a to a second end with the air ejection nozzle.