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We present a method to retrieve the absorption and backscattering coefficients of water from remote-sensing reflectance. Our method is based on semi-empirical modeling but does not require non-linear optimization methods which are sensitive to initial conditions. Instead, the equations are linearized and so can be solved using matrix inversion. The linearization is accomplished by two ways. Firstly, a linearized form of the basis function for phytoplankton pigment absorption is created. Secondly, the equations are solved for different spectral slopes, s, in the exponential function model for the absorption coefficient of dissolved organic matter and detritus, as well as, different spectral shapes, y, in the backscattering model. The linearized model is applied to the blue-green hyperspectral channels between 470 and 520 nm. The retrieved parameters are used to predict the remote-sensing reflectance for the channels in the wavelength bands between 600 and 650, and between 750 and 800 nm. The modeled values are compared to the actual values. In this way, the best fit s and y can be determined. The spectral bands 470-520, 600-650 and 750-800 nm have been chosen so as to minimize the effects of bottom reflectance in coastal waters. We tested our method on both synthetic data and field measurements.