NOVELTY - The system (150) has flanges (104), where each flange is provided with a surface (1042) for forming a stage with a shaft. The flange is provided with a shim (106) provided with a cam surface (1062). An outline of the cam surface in a plane that is radial relative to a rotational vertical axis is inclined relative to an angle (alpha). The flange is in direct engagement against the cam surface, by a portion (1046) of an external radial surface (1044). The shim is equipped with an oblong housing (1066) whose axis (X106) is parallel to the vertical axis.    USE - Adjustable system for guiding rotation of a shaft of a vertical axis rotating machine of a turbine such as Francis type turbine, a pump and a pump turbine, of a hydraulic to electrical power conversion installation (claimed). Can also be used for a shaft of an alternator or a motor.    ADVANTAGE - The flange is in direct engagement against the cam surface, by the portion of the external radial surface, so that position of the flange is defined by the direct engagement, according to a radial direction without being necessary to use an articulation with a kneecap and a reference block of effort as in materials of existing adjustable system while improving rigidity of support of the flange and reducing deformations of the shaft, and reducing transverse dimensions of the joints of wheel to labyrinth used in the installation incorporating the adjustable system. The adjustable system is inexpensive and simplifies clearance adjustment of a pedestal bearing while reducing immobilization set-up time of a vertical axis rotating machine.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for an installation for converting hydraulic power into electrical power.    DESCRIPTION OF DRAWING(S) - The drawing shows an exploded perspective view of a flange guidance system.    Axis of housing (X106)    Angle (alpha)    Flanges (104)    Shim (106)    Adjustable system (150)    Flange surface (1042)    External radial surface (1044)    Portion of an radial surface (1046)    Cam surface (1062)    Oblong housing (1066)