This paper addresses the problem of adaptively optimizing a two-channel lossless finite-impulse-response (FIR) filter bank, which finds application in subband coding and wavelet signal analysis. Instead of using a gradient decent procedure-with its inherent problem of becoming trapped in local minima of a nonquadratic cost function-two eigenstructure algorithms are proposed. Both algorithms feature a priori bounds on the output variance at any convergent point, which, based on simulations, lead to solutions that lie acceptably close to a global minimum point of an output variance objective function. Moreover, a sufficient condition for such stationary points based on fixed-point theory is shown. It is shown that the convergence rate of both algorithms increases as the separation of eigenvalues of the input covariance matrix increases. Simulations for synthetic and real data support the conclusions