The paper introduces both a new internal FM antenna for mobile phones based on the fractal Hilbert curve, and a new evaluation criterion for quantifying the quality of the signal received by the FM antenna of mobile phones. The main attribute of the new internal FM antenna is its reduced size; which is only 30*10*1 mm3. The measurements demonstrate that the power received by the internal FM antenna is 20 dB lower than the power received by the external wire antenna under the same measurement conditions. Despite the reduction of the power level, the evaluation criterion reveals that, owing to the threshold effect in FM receivers, the signal quality indicator is similar for both antennas. Additionally, the value of the signal quality indicator achieved by both antennas guarantees to listen to the FM radio channels clearly without noise nuisance and without interferences.