A catheter needle tip protector which assures that the needle is secured against accidental punctures after it is withdrawn from a patient's body. A catheter comprises a catheter hub, and a needle tip protector positioned within the catheter hub. A catheter needle defines a needle tip, with the needle being secured to a needle housing by first and second unequal biasing wires which extend between the needle housing and the needle tip protector. When the needle is withdrawn from the catheter hub, the first and second biasing wires extend the needle tip protector relative to the needle to an oblique position caused by the unequal biasing in which the needle tip is positioned within the needle tip protector. The first and second unequal biasing wires can comprise first and second coiled wires, which can have different biasing strengths to bias the needle tip protector to the oblique position, or can have different lengths to bias the needle tip protector to the oblique position. In one embodiment, the first and second coiled wires are encased within a sleeve in a bellows-like structure.