The invention relates to a cutting device for, in a cutting direction, cutting a belt layer from a web of unvulcanised rubber having mutually substantially parallel cords that are at a cord angle, comprising: a blade which sideward with respect to the cutting direction, is freely movable; a first detector for during cutting detecting a sideward displacement of the +0d5; a control computer, operationally coupled to the first detector, for giving control instructions on the basis of displacement information from the detecting means regarding sideward displacement of the +0d5; at least one actuator, operationally coupled to the control means for during cutting adjusting the cutting direction of the +0d5 on the basis of the control instructions.