A new algorithm for computing the accurate values of quasinormal frequ
encies of extremal Reissner-Nordstrom black holes is presented. The nu
merically computed values are consistent with the values earlier obtai
ned by Leaver and those obtained through the WKB method. Our results a
re more precise than other results known to date. We also find the cur
ious fact that the resonant frequencies of gravitational waves with a
multipole index l coincide with those of electromagnetic waves with a
multipole index l-1 in the extremal limit.