In this letter we present a new method for mitigating narrowband interference in orthogonal frequency-division multiplexing-based ultra-wideband communication systems. The proposed narrowband interference avoidance (NBIA) method performs spectral shaping of the transmitted signal using binary signature sequences with minimum total squared correlation (TSC) to avoid the narrowband interfering signal. We illustrate the proposed method with plots that show the spectrum of the transmitted signal with and without NBIA, and also present numerical results obtained from simulations showing improvement in the bit error rate (BER) performance of the system when NBIA is employed.