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A new bandlimited two-parameter Kautz basis, for application to reduced-order modeling (ROM), is proposed. It is derived from the original Kautz basis by means of a pertinent rational frequency transformation, and is shown to be orthonormal over a narrowband frequency interval. By means of obliquely projecting a general Mth-order state space transfer function onto this bandlimited Kautz basis, we obtain a new ROM technique, which does not belong to the class of Krylov methods, but to the rather more general family of oblique projection techniques. Pertinent features of the new method are the reduction in computational effort and the fact that a more efficient ROM approach is obtained by focusing on the frequency band under scrutiny. The robustness and accuracy of the new method is illustrated by applying it to a number of benchmark examples.