We present a new technique for processing speckle interferometric data is presented, which uses the CLEAN algorithm, originally developed for the removal of the effects of incomplete spatial frequency coverage in aperture synthesis radio maps. Since Labeyrie first noted in 1970 that the autocorrelation of a speckle-gram preserves information up to the diffraction limit of an optical telescope, a number of different techniques have been applied to recover this information, usually by Fourier deconvolution of the average power spectrum of the specklegrams with a similar spectrum for a known point source. An alternative is to deconvolve the average autocorrelation of the specklegrams directly, rather than the power spectrum; this is where CLEA...