Cosmoclostis quadriquadra is a moth of the Pterophoridae family. It is found on Christmas Island, a territory of Australia in the Indian Ocean. The wingspan is 11–13 mm. The antennae are white and the head is pale rust-brown above, with a white face. The thorax is yellowish white anteriorly and rusty-brown posteriorly. The underside is shining white, tinged with yellowish at the sides. The forewings are yellowish white. The hindwings are bronzy grey.