A novel depolarizing chipless tag configuration with high angular insensitivity is presented. The basic tag comprises two dipole resonators arranged with a relative rotation of 45°. The proposed configuration improves the depolarization properties performance of a single dipole over the ground plane which provides a peak with perfect polarization conversion only if the electric field impinges at 45° with respect to the dipole resonator. The second dipole arranged at 45° compensates the cross-polar reduction which is observed when the electric field is not correctly polarized. Indeed, when the field is tilted by 90° with respect to the first dipole, it forms an angle of 45° with the second one. The proposed configuration is also analyzed for providing multiple frequency peaks. A tag with 4 angular independent frequency peaks laying between 2 GHz and 5.5 GHz is designed. Angular frequency maps are used to illustrate the peculiar frequency shifts achieved when the electric fields rotate in the plane of the dipole. Finally, a prototype of the polarization insensitive tags is fabricated and measured to confirm the simulated results.