Method for manufacturing a tyre by means of an assembly comprising: - a first structure of first filamentary elements (64, 66), the first structure of first filamentary elements (64, 66) extending in a first general direction, - a second structure of second filamentary elements (68, 70), - a supporting structure comprising supporting filamentary elements connecting the first structure of first filamentary elements (64, 66) and the second structure of second filamentary elements (68, 67) to one another, in which method the assembly is wound, around an assembly support substantially of revolution about an axis of revolution (YY'), in the circumferential direction (XX') of the assembly support, which method is characterized in that, at the latest during the winding step, the first structure of first filamentary elements (64, 66) has at least one transverse discontinuity extending transversely continuously over the whole width of the first structure of first filamentary elements (64, 66), the or each transverse discontinuity being defined by a pair of two transverse edges (102, 104) each extending transversely over the whole width of the first structure of first filamentary elements (64, 66) and each situated on either side of the or each transverse discontinuity in the first general direction, in that, subsequent to the winding step, the first structure of first filamentary elements (64, 66) is separated radially with respect to the axis of revolution (YY') of the assembly support in such a way as to move each transverse edge (102, 104) of each pair away from one another in the circumferential direction (XX') of the assembly support such that the first structure of first filamentary elements (64, 66) is lengthened in the circumferential direction (XX') of the assembly support. - a first structure of first filamentary elements (64, 66), the first structure of first filamentary elements (64, 66) extending in a first general direction, - a second structure of second filamentary elements (68, 70), - a supporting structure comprising supporting filamentary elements connecting the first structure of first filamentary elements (64, 66) and the second structure of second filamentary elements (68, 67) to one another, in which method the assembly is wound, around an assembly support substantially of revolution about an axis of revolution (YY'), in the circumferential direction (XX') of the assembly support, which method is characterized in that, at the latest during the winding step, the first structure of first filamentary elements (64, 66) has at least one transverse discontinuity extending transversely continuously over the whole width of the first structure of first filamentary elements (64, 66), the or each transverse discontinuity being defined by a pair of two transverse edges (102, 104) each extending transversely over the whole width of the first structure of first filamentary elements (64, 66) and each situated on either side of the or each transverse discontinuity in the first general direction, in that, subsequent to the winding step, the first structure of first filamentary elements (64, 66) is separated radially with respect to the axis of revolution (YY') of the assembly support in such a way as to move each transverse edge (102, 104) of each pair away from one another in the circumferential direction (XX') of the assembly support such that the first structure of first filamentary elements (64, 66) is lengthened in the circumferential direction (XX') of the assembly support.