In order to install a reinforcement around a cylindrical underground pipeline, an excavation coffer is laid on the ground above the pipeline, at the same time placing transversely to the pipeline front and rear faces of the coffer, each having along its lower edge an indentation of a shape adapted to the cylindrical shape of the cylindrical pipeline, the coffer is buried in the ground substantially until the indentations are brought up against the pipeline, soil material is removed between the front and rear faces of the coffer in order to give access to an upper part of the wall of the pipeline, a duct in the form of an arc of a circle is engaged under the pipeline, at the same time being pushed along the lower part of the wall of the pipeline, a prestressing reinforcement is threaded into this duct, and the armature is clamped and anchored around the pipeline.