The present invention relates to a windscreen wiper 1 comprising a wiper blade 10 made of supple material which is supported by a flexible structure 20, the wiper blade 10 comprising a lip 12 mounted so that it can pivot back and forth on either side of the plane of the wiper. The invention is notable in that the lip 12 is able to press against the support structure 20 when the wiper 1 is brought laterally into contact with a surface that is to be wiped, and in that said wiper 1 further comprises buffer means 40 which are secured to the support structure 20 and which are able to deaden the contact between the lip 12 and said support structure 20.