Disclosed is a comb having a lamellar body and including, along a toothed edge, teeth able to penetrate the coat of hair. The comb eliminates injuries caused to the animal by sharp teeth, eliminating fur damage while also 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 of the two sets of teeth A and B, which are positioned one on each side of the mid plane P of the body 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 and a curved extreme internal face, the tooth set B being finer and provided with shorter teeth.