We demonstrate experimentally the full tunability of a coherent femtosecond source in the whole ultraviolet spectral region. The experiment relies on the technique of high-order harmonic generation driven by a near-infrared parametric laser source in krypton gas. By tuning the drive wavelength in the range between 1100 to 1900 nm, we generated intense harmonics from near to extreme ultraviolet. A number of photons per shot of the order of 10^7 has been measured for the first harmonic orders. Many novel scientific prospects are expected to benefit from the use of such a table-top tunable source.