A system for guiding a mobile carriage in a frame. The frame has three parallel linear-guiding tracks including a first track extending centrally on the frame and second and third tracks arranged laterally of the first track. The carriage has at least two axes of rotation. A first axis drives at least a first wheel in the first guiding track and a second axis drives at least a second wheel and at least a third wheel, respectively, in the second and third guiding tracks. The two axes of rotation are perpendicular. The description also relates to an associated method. A primary object is to enable the end of a mobile beam, such as a beam carrying a device for wiping a galvanizing product off a steel strip, to perform a guided movement with a high degree of freedom while minimizing mechanical stresses.