A heating device for a floor includes a membrane, a plurality of heating elements attached to the membrane, at least one positively charged electrode attached to each of the heating elements and at least one negatively charged electrode attached to each of the heating elements, where the at least one positively charged electrode and the at least one negatively charged electrode are connected to an electrical power source and supply electrical power to the heating elements. The heating elements, the at least one positively charged electrode and the at least one negatively charged electrode are arranged on the membrane so that cutting of the membrane along a cutting line in any direction across the membrane does not disrupt the supply of electrical power to the heating elements.