We present for the first time ever, a perfect electrostatic anti-spring. This electrostatic actuator is a symmetric double-sided comb-drive with uniform-width fingers and a linear tapering of the lengths of the rotor fingers. When both stators are grounded and a constant dc bias is applied to the rotor, this actuator induces a diverging electrostatic force which is a perfectly linear function of displacement. This force is exactly the opposite of the restoring force in a linear spring, and hence we refer to it as a linear anti-spring. The new design is superior in terms of design robustness and sensitivity to fabrication imperfections, relative to comb-drives with shaped fingers which have been used for similar purposes. We demonstrate the performance of the new anti-spring, by using it to continuously and reversibly down-tune the natural frequency of a linear mechanical system. Experimental data exhibit excellent fit between predictions and measurements.