A reversible orthosis is configured to support and/or immobilize at least one limb of a patient, including a textile article with first and second faces. The faces are equally able to contact a limb or limbs of the patient. The device includes at least one fastening tab having an active face with fastening elements cooperable with first or second securing device arranged respectively on the first and second faces and an inactive face opposite the active face. The fastening tab is fixed non-removably via its inactive face on a zone of the textile article contiguous to one of the edges of the textile article, allowing a 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 device, and a second position, in which the active face catches by contact on the second securing device.