We obtain a robust, non-parametric, estimate of the Hubble constant from the linear diameters and rotation velocities of galaxies in the recent KLUN sample, calibrated using Cepheid distances to Hubble Space Telescope Key Project galaxies. There are two key features that make our analysis considerably more robust than previous work. First, the method is independent of the spatial distribution of galaxies and is insensitive to Malmquist bias. It may, therefore, be applied to more distant samples than so-called `plateau' methods - making it much less vulnerable to the impact of peculiar motions in the Local Supercluster. Secondly, we include information on the galaxy rotation velocities in a fully non-parametric manner: unlike the conventional Tully-Fisher relation we reconstruct a robust estimate of the cumulative distribution function of galaxy diameter at given rotation velocity, without requiring the assumption of, for example, a linear Tully-Fisher relation with symmetric Gaussian residuals. Using this robust method we find $H_0=65\pm 6$ km.s$^{-1}$.Mpc$^{-1}$ from our analysis - in excellent agreement with many recent determinations of the Hubble parameter, although somewhat larger than previous results using galaxy diameters.