We report on the preparation, atomic resolution imaging, and element selective damage mechanism in atomically thin boron nitride membranes. Flakes of less than 10 layers are prepared by mechanical cleavage and are thinned down to single layers in a high-energy electron beam. At our beam energies, we observe a highly selective sputtering of only one of the elements and predominantly at the exit surface of the specimen, and then subsequent removal of atoms next to a defect. Triangle-shaped holes appear in accordance with the crystallographic orientation of each layer. Defects are compared to those observed in graphene membranes. The observation of clean single-layer membranes shows that hexagonal boron nitride is a further material (in addition to graphene) that can exist in a quasi-two-dimensional allotrope without the need for a substrate.