The estimation of frequency response function from experimental data containing noise forms the basis for the generation of experimental modal models of linear structures. A number of authors have documented that the current methods of estimating the frequency response function produces bias errors in the estimate. An alternative method is discussed that estimates the frequency response function by simultaneously minimizing the uncorrelated content associated with the input measurement and the uncorrelated content associated with the response measurement. A closed form solution is presented for a single input/output model along with a redefinition of the ordinary coherence functions. Experimental implementation of the estimating process is discussed and illustrated using measured laboratory data. The unbiasing character of this bivariate error analysis method allows the true estimation of a frequency response function from experimental data containing random error.