The contributions of this paper are twofold. The first is to give theoretical motivation for whitening in the recently proposed adaptive filtering algorithm named the Krylov-proportionate normalized least-mean-square (KPNLMS) algorithm. The second is to present the details of whitening in KPNLMS (In the original work of KPNLMS, the whitening procedure is mentioned but is not described in detail). An interesting connection among the transform-domain adaptive filter (TDAF), proportionate normalized least-mean-square (PNLMS), and KPNLMS algorithms is also provided. Numerical examples demonstrate that KPNLMS drastically outperforms TDAF especially in noisy situations.