Scanning tunneling microscopy measurements of height profiles, along the chains of Si atoms on the terrace edges of a perfectly ordered Si(553)-Au surface, reveal an STM bias-dependent mixed periodicity with periods of one, two and one and a half lattice constants. The simple linear chain model usually observed with STM cannot explain the unexpected fractional periodicity in the height profile. It was found that the edge Si chain stands for, in fact, a zigzag structure, which is composed of two neighboring rows of Si atoms and was detected in the STM experiments. Tight-binding calculations of the local density of states and charge occupancy along the chain explain the voltage-dependent modulations of the STM profiles and show that oscillation periods are determined mainly by the surface and STM tip Fermi energies.