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We report a new deconvolution method for fluorescence lifetime imaging microscopy (FLIM) based on the Laguerre expansion technique. The performance of this method was tested on synthetic and real FLIM images. The following interesting properties of this technique were demonstrated. 1) The fluorescence intensity decay can be estimated simultaneously for all pixels, without a priori assumption of the decay functional form. 2) The computation speed is extremely fast, performing at least two orders of magnitude faster than current algorithms. 3) The estimated maps of Laguerre expansion coefficients provide a new domain for representing FLIM information. 4) The number of images required for the analysis is relatively small, allowing reduction of the acquisition time. These findings indicate that the developed Laguerre expansion technique for FLIM analysis represents a robust and extremely fast deconvolution method that enables practical applications of FLIM in medicine, biology, biochemistry, and chemistry.