Tread band made of rubber-like material for a tyre. The tread band comprises a plurality of blocks (3), each block (3) having a contact face (5) designed to come into contact with the ground when the tyre travels and a plurality of lateral faces (7). Each block (3) comprises a main sipe (9) extending along a main direction. Each block (3) comprises a plurality of secondary sipes (13) perpendicular to the main sipe (9). Each lateral face (7) of the block (3) is covered by a layer (15) of covering material over at least 50% of the surface of this lateral face (7). The covering material has a modulus of elasticity which is greater than the modulus of elasticity of the rubber-like material forming the block (3). The main sipe (9) and/or each secondary sipe (13) has/have an expanded portion (17) in the depth of the block (3).