The use of data averaging to improve the angular precision of electron backscattered diffraction (EBSD) maps is discussed. It is shown that orientations may be conveniently and rapidly averaged using the four Euler-symmetric parameters which are coefficients of a quaternion representation. The processing of EBSD data requires the use of an edge preserving filter and a modified Kuwahara filter has been successfully implemented and tested. Three passes of such a filter have been shown to reduce orientation noise by a factor of ∼10. Application of the method to deformed and recovered aluminium alloys has shown that such data processing enables small subgrain misorientation (< 0.5°) to be detected reliably.