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We stabilize an ultraviolet diode laser system at 369.5 nm to the optical absorption signal from Yb+ ions in a hollow-cathode discharge lamp. The error signal for stabilization is obtained by Zeeman spectroscopy of the 3 GHz wide absorption feature. The frequency stability is independently measured by comparison to the fluorescence signal from a laser-cooled crystal of Y 174 b+ ions in a linear Paul trap. We measure a frequency fluctuation of 1.7 MHz over 1000 s and a frequency drift of 20 MHz over 7 days. Our method is suitable for use in quantum information processing experiments with trapped ion crystals.