A modified matrix model describing transfer of excitation energy in the photosynthetic pigment system is discussed. In addition to the antenna pigments and reaction centers of the simple matrix model, a coupling complex is postulated mediating energy transfer between antenna and reaction centers. The values of the parameters describing the transfer properties of the coupling complex can be chosen in such a way that a number of recent unexplained measurements of fluorescence properties of various purple bacteria can be described. If such coupling complexes are present in oxygen evolving organisms, some of their properties must be different from those of purple bacteria.