The capacitance technique is one of the simplest methods to determine the dielectric constant of dielectric sheets in the low-frequency band. A new methodology and test procedure which eliminates the effect of the capacitors from the calculations and improves the accuracy of measurement is introduced. The main advantage of the method is that it can be applied for arbitrary-shaped dielectric sheets as long as they are smaller than approximately 0.6 of the diameter of the capacitor. The presented measurement results show the effectiveness of the method on measurement. A prototype version of the setup helped us achieve 7% accuracy.