A folding machine for folding a stack of sheets, the folding machine comprising: a frame; mechanism for pre-folding a stack of sheets along a crease line into a main plane such that a booklet with a straight back is obtained; mechanism for keeping the pre-folded booklet relative to the frame; mechanism for finishing the fold; and a transport plate having a leading edge around which the stack of sheets is folded, the transport plate being movable along the mechanism for pre-folding and the mechanism for finishing the fold.