Experimental studies were carried out on fully developed and steady electro-osmotic flow in a rectangular channel where the channel height $h$ is comparable to its width and the thickness of the electric double layer characterized by the Debye length is much less than $h$. The nano-particle image velocimetry technique was used to measure the two components of the velocity field parallel to and within about 100 nm of the channel wall for $h\,{\leq}\,25\,\umu$m. The mobility of the particle tracers was calculated from averaged velocity data for various electric field strengths. The experimentally determined mobility values are compared with analytical predictions for dilute aqueous solutions of sodium tetraborate.