We report experimental results and a theoretical analysis of the Debye length in aqueous solutions of nonadsorbing polyelectrolytes. The measurements were done using a surface forces apparatus, in which the normal forces between smooth mica surfaces in aqueous hyaluronic acid (HA) solutions were measured as a function of surface separation (to +/-1 Angstrom). HA is negatively charged and does not adsorb to the negatively charged surface of mica, as was established by optical and viscosity measurements and in agreement with the measured force-distance curves. From these measurements it appears that the multivalent polyelectrolyte is "depleted" from the gap between the surfaces. We use the mean-field Poisson-Boltzmann theory to theoretically predict the effective Debye length and double-layer force under such conditions and compare the predictions with the experimental results. The comparison gives excellent agreement and shows that the effective Debye length is determined solely by the monovalent ions in the solution. Specifically, the effective Debye length K-eff(-1) for the double-layer interaction is determined by an effective ionic concentration given by rootn(s)n(c), where n(s) and n(c) are the bulk negative and positive monovalent ion concentrations, respectively.