Tyre of substantially toric shape about an axis of revolution, comprising a crown, two sidewalls and two beads, each sidewall connecting each bead to the crown, the tyre comprising at least one continuous filamentary reinforcing element (38, 39, 40) comprising N≥2 circumferential turns about the axis of revolution which are radially superposed on one another, the continuous filamentary reinforcing element (38, 39, 40) comprising a radially outer free end (E1, E3) and a radially inner free end (E2, E4), the continuous filamentary reinforcing element (38, 39, 40) extending radially at least in part in one of the two beads, characterized in that at least one of conditions I and II is satisfied: I - the radially outer free end (E1, E3) is, at the azimuth (AzO; Az0') of the radially outer free end (E1, E3), arranged radially between: - at least one first portion (50, 60) of the continuous filamentary reinforcing element (38, 39, 40), this first portion (50, 60) being arranged radially on the outside of the radially outer free end (E1, E3), and - at least one second portion (52, 62) of the continuous filamentary reinforcing element (38, 39, 40), this second portion (52, 62) being arranged radially on the inside of the radially outer free end (E1, E3), II - the radially inner free end (E2, E4) is, at the azimuth (AzO; Az0") of the radially inner free end (E2, E4), arranged radially between: - at least one first portion (54, 64) of the continuous filamentary reinforcing element (38, 39, 40), this first portion (54, 64) being arranged radially on the outside of the radially inner free end (E2, E4), and - at least one second portion (56, 66) of the continuous filamentary reinforcing element (38, 39, 40), this second portion (56, 66) being arranged radially on the inside of the radially inner free end (E2, E4). I - the radially outer free end (E1, E3) is, at the azimuth (AzO; Az0') of the radially outer free end (E1, E3), arranged radially between: - at least one first portion (50, 60) of the continuous filamentary reinforcing element (38, 39, 40), this first portion (50, 60) being arranged radially on the outside of the radially outer free end (E1, E3), and - at least one second portion (52, 62) of the continuous filamentary reinforcing element (38, 39, 40), this second portion (52, 62) being arranged radially on the inside of the radially outer free end (E1, E3), - at least one first portion (50, 60) of the continuous filamentary reinforcing element (38, 39, 40), this first portion (50, 60) being arranged radially on the outside of the radially outer free end (E1, E3), and - at least one second portion (52, 62) of the continuous filamentary reinforcing element (38, 39, 40), this second portion (52, 62) being arranged radially on the inside of the radially outer free end (E1, E3), II - the radially inner free end (E2, E4) is, at the azimuth (AzO; Az0") of the radially inner free end (E2, E4), arranged radially between: - at least one first portion (54, 64) of the continuous filamentary reinforcing element (38, 39, 40), this first portion (54, 64) being arranged radially on the outside of the radially inner free end (E2, E4), and - at least one second portion (56, 66) of the continuous filamentary reinforcing element (38, 39, 40), this second portion (56, 66) being arranged radially on the inside of the radially inner free end (E2, E4). - at least one first portion (54, 64) of the continuous filamentary reinforcing element (38, 39, 40), this first portion (54, 64) being arranged radially on the outside of the radially inner free end (E2, E4), and - at least one second portion (56, 66) of the continuous filamentary reinforcing element (38, 39, 40), this second portion (56, 66) being arranged radially on the inside of the radially inner free end (E2, E4).