A new diffracted-beam monochromator has been developed for Bragg-Brentano X-ray diffractometers equipped with a linear detector. The monochromator consists of a cone-shaped graphite highly oriented pyrolytic graphite crystal oriented out of the equatorial plane such that the parafocusing geometry is preserved over the whole opening angle of the linear detector. In our standard setup a maximum wavelength discrimination of 3% is achieved with an overall efficiency of 20% and a small decrease in angular resolution of only 0.02 °2θ. In principle, an energy resolution as low as 1.5% can be achieved.