A new approach to solving steady state data reconciliation problems with bilinear constraints is proposed. Previously it was shown by Crowe that these problems can be solved using the method of matrix projection. In this work the objective function and its constraints are put into unconstrained form using Lagrange multipliers. Unconstrained optimization methods based on analytical derivatives are then used to solve the unconstrained formulation. The unconstrained approach is tested on two different reconciliation problems from the literature using a number of Newton-type unconstrained optimization methods. The unconstrained methods are compared in terms of robustness and efficiency in solving the example problems. The performance of the unconstrained approach is compared to that of the method of matrix projection and tile projected Lagrangian algorithm implemented in GAMS/MINOS.