Rotation symmetric Boolean functions(RSBFs) have been used as components of different cryptosystems.In this paper,we investigate n-variable(n even and n≥12) RSBFs to achieve maximum algebraic immunity(AI),and provide a construction of RSBFs with maximum AI and nonlinearity.These functions have higher nonlinearity than the previously known nonlinearity of RSBFs with maximum AI.We also prove that our construction provides high algebraic degree in some case.