An assembly of an identification unit, more particularly an activity meter for identifying an animal and possibly measuring movements of an animal to which the identification unit, in use, is fastened, and a fastening strap, connected with the identification unit, for fastening the identification unit to the neck or a leg of the animal, the fastening strap being provided with a first and second free end, the assembly being further provided with a closing member comprising a slotted tunnel, while, in use, the strap forms a loop and at a position where a first part and a second part of the strap overlie each other, is enclosed by the tunnel, the assembly being further provided with first fastening means for connecting the first part and the closing member with each other, and second fastening means for fastening the second part to the first part and/or the closing member, with at least a part of the second fastening means, in use, being situated in the tunnel.