A new model is presented to construct a realistic form for the joint-scalar probability density function, as opposed to assuming its shape, with application to the moment equation solution of turbulent (non-premixed) combustion. The model approximates the thermo-chemical pdf in a general turbulent reacting flow by the scalar pdf that decayed from an initial binary field in homogeneous turbulence, parameterized by an appropriate set of lower moments. Full resolution, complex chemistry, scalar decay simulations are achieved with the computationally affordable Linear Eddy Model. The constructed pdf, in contrast to the assumed shape approach, incorporates the underlying physics of advection by all turbulent scales, molecular diffusion and chemical reaction. The constructed pdf has no adjustable constants or calibration factors, and its tabulation allows the expensive turbulence-chemistry interactions to be decoupled from the moment equation solution. In ana-prioriexperimental comparison using a two variable chemical mechanism, the constructed pdf shows qualitative superiority over a common assumed shape pdf. In application to the steady-state solution of a turbulent, hydrogen, round jet flame, the model demonstrates comparative agreement with the conventional assumed shape pdf, and predicts improved OH concentration fluctuation intensity.