We report on experimental studies of divergence of proton beams from nanometer thick diamond-like carbon (DLC) foils irradiated by an intense laser with high contrast. Proton beams with extremely small divergence (half angle) of 2 degree are observed in addition with a remarkably well-collimated feature over the whole energy range, showing one order of magnitude reduction of the divergence angle in comparison to the results from micrometer thick targets. We demonstrate that this reduction arises from a steep longitudinal electron density gradient and an exponentially decaying transverse profile at the rear side of the ultrathin foils. Agreements are found both in an analytical model and in particle-in-cell simulations. Those novel features make nm foils an attractive alternative for high flux experiments relevant for fundamental research in nuclear and warm dense matter physics.