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This paper describes the construction of a matrix expressing the response of a large sodium iodide crystal to axially incident 0.01 to 8-mev gamma rays. Interpolation from measured and calculated pulse-height distributions due to monoergic sources yielded a series of distributions at source-energy intervals uniform in the square root of energy. Each distribution was normalized to the total detection efficiency of the crystal and divided into "bins" whose centers were spaced at the above source-energy intervals. Integrated values of the contents of all such bins were written as a triangular matrix. Inversion of this matrix was performed on an automatic computer. Reduction of an experimental pulse-height distribution to a spectrum is effected by first expressing the distribution as a series of bin contents as above, then multiplying this series by the inverse response matrix, and finally dividing by bin widths to give photons per mev.