Braking system for a vehicle combination, consisting of a tractor vehicle with a tractor vehicle brake and a trailer vehicle with a trailer brake, the tractor vehicle having an ignition system for a drive engine of the tractor vehicle supplied from an electrical energy accumulator of the tractor vehicle, the braking system being operated by pressure medium, having a trailer control valve and a parking brake module which are electrically controllable, and having an electronic control unit for the control of the trailer brake of the trailer vehicle, electrically connected to the trailer control valve and to the parking brake module, the parking brake module being connected, in a manner which conducts pressure medium, on the input side to a pressure medium accumulator of the braking system of the vehicle combination and on the output side to a control pressure input of the trailer control valve for the switchable pressurization or depressurization of the control pressure input of the trailer control valve, and the parking brake module having a redundancy circuit for the pressurization or depressurization of the control pressure input of the trailer control valve even for the case of a malfunction or a failure of the electronic control unit, characterized in that the parking brake module comprises a first directional valve configured as a control valve, a second directional valve configured as a redundancy valve and a pressure- controlled changeover valve, - the control valve and the redundancy valve being respectively connected, in a manner which conducts pressure medium, on the input side to the pressure medium accumulator and on the output side to a respective input (P17, P18) of the changeover valve, - one output of the changeover valve being connected, in a manner which conducts pressure medium, to the control pressure input of the trailer control valve, so that an input pressure at one or both inputs (P17, P18) of the changeover valve can be passed through to the control pressure input of the trailer control valve, - the control valve being switchably connectable by means of a first electrical switching device to the electrical energy accumulator of the tractor vehicle, - the redundancy valve being switchably connectable by means of a second electrical switching device to the electrical energy accumulator and to the ignition system of the tractor vehicle, - in a first switching position of the control valve and/or the redundancy valve, the pressure medium accumulator being blocked off from the control pressure input of the trailer control valve and, in a second switching position of the control valve and/or the redundancy valve, the pressure medium accumulator being connected, in a manner which conducts pressure medium, to the control pressure input of the trailer control valve, - and in that the electronic control unit comprises an electronic switch unit with a latching function, - the redundancy valve and the control valve being electronically inter-connected by means of this switch unit and the redundancy valve being controllable, - the latching function saving the respective current first switching position or second switching position of the redundancy valve or the control valve, - so that, in the event of a recognized malfunction or a failure of the electronic control unit, the last error-free switching position of the control valve or the redundancy valve is latched so long as the electronic control unit does not switch to an operationally safe resting state or the ignition system is not switched off. - the control valve and the redundancy valve being respectively connected, in a manner which conducts pressure medium, on the input side to the pressure medium accumulator and on the output side to a respective input (P17, P18) of the changeover valve, - one output of the changeover valve being connected, in a manner which conducts pressure medium, to the control pressure input of the trailer control valve, so that an input pressure at one or both inputs (P17, P18) of the changeover valve can be passed through to the control pressure input of the trailer control valve, - the control valve being switchably connectable by means of a first electrical switching device to the electrical energy accumulator of the tractor vehicle, - the redundancy valve being switchably connectable by means of a second electrical switching device to the electrical energy accumulator and to the ignition system of the tractor vehicle, - in a first switching position of the control valve and/or the redundancy valve, the pressure medium accumulator being blocked off from the control pressure input of the trailer control valve and, in a second switching position of the control valve and/or the redundancy valve, the pressure medium accumulator being connected, in a manner which conducts pressure medium, to the control pressure input of the trailer control valve, - and in that the electronic control unit comprises an electronic switch unit with a latching function, - the redundancy valve and the control valve being electronically inter-connected by means of this switch unit and the redundancy valve being controllable, - the latching function saving the respective current first switching position or second switching position of the redundancy valve or the control valve, - so that, in the event of a recognized malfunction or a failure of the electronic control unit, the last error-free switching position of the control valve or the redundancy valve is latched so long as the electronic control unit does not switch to an operationally safe resting state or the ignition system is not switched off.