This orthopedic orthosis, includes a textile article with first and second faces; the orthosis can be fitted in place such that either the first and second faces can equally well contact a patient limb. The orthosis has at least one fastening tab including an active face with fastening elements that may cooperate with first or second securing means arranged respectively on the first the second faces 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 contiguous to an edge of the textile article, so as to be able to pivot about an 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.