Reversible orthosis

An orthopedic orthosis which can support and/or immobilize at least one limb of a patient, comprising a textile article with first and second faces, either of which first and second faces can equally well come into contact with the limb or limbs of the patient, wherein the orthosis additionally has at least one fastening tab comprising an active face with fastening elements that are able to cooperate with first or second securing means arranged respectively on the first face and the second face of the textile article, and an inactive face opposite the active face, said fastening tab being fixed non-removably via its inactive face on a zone of the textile article contiguous to one of the edges of said textile article, so as to be able to pivot, about a pivot axis substantially parallel to this edge, between a first position, in which the active face catches by contact on the first securing means, and a second position, in which the active face catches by contact on the second securing means.