We study the electrical conductance of gold nanoconstrictions by controlling the electrochemical potential. At positive potentials, the conductance is quantized near integer multiples of G0(2e(2)/h) as shown by well-defined peaks in the conductance histogram. Below a certain potential, however, additional peaks near 0.5G(0) and 1. 5G(0) appear in the histogram. The fractional conductance steps are as stable and well defined as the integer steps. The experimental data are discussed in terms of electrochemical-potential-induced defect scattering and Fermi energy shift, but a complete theory of the phenomenon is yet to be developed.