Usually the mel-frequency cepstral coefficients (MFCCs) are derived via Hamming windowed DFT spectrum. In this paper, we advocate to use a so-called multitaper method instead. Multitaper methods form a spectrum estimate using multiple window functions and frequency-domain averaging. Multitapers provide a robust spectrum estimate but have not received much attention in speech processing. Our speaker recognition experiment on NIST 2002 yields equal error rates (EERs) of 9.66 % (clean data) and 16.41 % (-10 dB SNR) for the conventional Hamming method and 8.13 % (clean data) and 14.63 % (-10 dB SNR) using multitapers. Multitapering is a simple and robust alternative to the Hamming window method.