We report sensitive VLA 3.6 cm radio observations toward the head of the Cone Nebula in NGC 2264, made in 2006. The purpose of these observations was to study a non-thermal radio jet recently discovered, which appears to emanate from the head of the Cone Nebula. The jet is highly polarized, with well-defined knots, and one-sided. Comparison of our images with 1995 archive data indicates no evidence of proper motions or polarization changes. We find reliable flux density variations in only one knot, which we tentatively identify as the core of a quasar or radio galaxy. An extragalactic location seems to be the best explanation for this jet.