The fluid machine includes a stationary member (6), a rotary member (5) and a labyrinth seal (9) including a succession of stationary steps (11) formed on the stationary member (6), and a succession of rotary steps (14) formed on the rotary member (5). The labyrinth seal (9) further includes a plurality of stationary recesses (18) each formed in a radial wall portion (12) of a respective stationary step (11), and a plurality of rotary recesses (21) each formed in a radial wall portion (16) of a respective rotary step (14). Each stationary step (11) defines a stationary projection (19) delimited by the stationary recess (18) formed on said stationary step (11), and each rotary step (14) defines a rotary projection (22) delimited by the rotary recess (21) formed on said rotary step (14). The axial width (Wr) of each of the stationary recesses (18) and of the rotary recesses (21) substantially equals the axial width (Wp) of each of the stationary projections (19) and of the rotary projections (22).