The polarized thermal emission from diffuse Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100?GHz. In this paper we exploit the uniqueness of the Planck HFI polarization data from 100 to 353?GHz to measure the polarized dust angular power spectra ClEE and ClBB over the multipole range 40 <l< 600 well away from the Galactic plane. These measurements will bring new insights into interstellar dust physics and allow a precise determination of the level of contamination for CMB polarization experiments. Despite the non-Gaussian and anisotropic nature of Galactic dust, we show that general statistical properties of the emission can be characterized accurately over large fractions of the sky using angular power spectra. This level is the same magnitude as reported by BICEP2 over this l range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky.