We show that there is an absolute constant c > 1/2 such that the Mahler measure of the Fekete polynomials f p of the form(where the coefficients are the usual Legendre symbols) is at least c √ p for all sufficiently large primes p. This improves the lower bound 1 2 − ε √ p known before for the Mahler measure of the Fekete polynomials f p for all sufficiently large primes p ≥ c ε . Our approach is based on the study of the zeros of the Fekete polynomials on the unit circle.