A mower includes a traction frame that supports at least one cutting unit and a grass catcher associated with each cutting unit. The cutting unit and grass catcher are both operatively coupled to the traction frame such that they both jointly are able to steer or yaw together during turns of the traction frame. This permits the gap between the cutting unit and a grass basket which is part of the grass catcher to remain constant whether the traction frame is travelling straight or is turning. This ensures that the grass clippings will be properly retained in the grass basket without dribbling out of the grass basket. In addition, a system is provided for keeping the grass catcher level as it is lifted up out of engagement with the ground into a raised, transport position, also to better retain the grass clippings within the grass basket.