This hydraulic machine comprises a wheel supported by a shaft (5), the wheel and the shaft being able to rotate about a vertical axis (X5) while a radial hydrostatic or hydrodynamic bearing (100) is formed between, on the one hand, a radial peripheral surface (52) of the shaft and, on the other hand, an internal radial surface (102) of a member (101) that is fixed relative to the vertical axis. The bearing (100) extends between two edges (121, 122) which, in normal operation, constitute regions for the removal of a film of water formed in the bearing. At least one cavity (130) is created in the fixed member (101) and opens onto its internal radial surface (102) near a first edge (122) of the bearing. The machine comprises means (131, 132, 133) for placing the cavity (130) in fluidic communication with a volume (V1) situated outside the bearing near the second edge (121) of the bearing (100). That allows some (E2) of the film of water from the bearing (100) to be removed towards the second edge (121) if the bearing becomes obstructed near the first edge (122).