We characterize the holomorphic self-maps of the unit disk for which the corresponding composition operator is an isometry of BMOA equipped with the Möbius invariant (Formula presented.) norm, answering a question posed by Laitila, for (Formula presented.). Also, we show that the image of the symbol of an isometric composition operator for BMOA, with respect to the Möbius invariant (Formula presented.) norm, (Formula presented.), covers the whole unit disc except a set of zero logarithmic capacity.