A shear band for a tire includes an annular first, radially outer fabric layer extending circumferentially around the tire; and an annular second, radially inner fabric layer extending circumferentially around the tire. The shear band is formed from a single shear band strip helically wound circumferentially and axially with a first edge of the shear band strip. The first edge of the shear band strip has a first extension flap for engaging an opposite second edge of the shear band strip. The first extension flap is continuously secured to the opposite second edge linearly along the opposite second edge of the shear band strip.