The invention relates to a comb (1) having a lamellar body (2) and comprising, along a toothed edge, teeth able to penetrate the coat of hair. The object of the invention is to eliminate injuries caused to the animal by sharp teeth, to eliminate fur damage to the point of bald patches while on the other hand improving the treatment of the hair coat and to improve brushing performance by adapting to the hair coat of each animal, in each season. To this end, the teeth (7 and 8) of the two sets of teeth A and B, which are positioned one on each side of the mid plane P of the body (2) and the teeth of which sets are intercalated with one another, have anti-injury roundings at the tips and over part of the length of the edge corners leading from these tips and are delimited between a flat external face (9a, 9b) and a curved extreme internal face (10a and 10b), the tooth set B being finer and provided with shorter teeth (8).