The friction damper has been widely used to reduce the resonant vibration of blades. The most commonly used methods for studying the dynamic behavior of a blade with a friction damper are direct integration methods. Although the harmonic balance method (HBM) is a well-known method for studying nonlinear vibration problems, generally only a one-term approximation has been proposed to study the nonlinear vibration of a frictionally damped blade. In this work, a HMB procedure with a multiterm approximation is proposed. The results show that the steady-state response and other related behavior of a frictionally damped blade can be predicted accurately and quickly by an HBM with a multiterm approximation.