Using an abstract condition of Riesz basis generation of discrete operators in the Hilbert spaces, we show, in this paper, that sequence of generalized eigenfunctions of an Euler Bernoulli beam equation with tip mass under boundary linear feedback control forms Riesz basis for the state Hilbert space. In the meanwhile, an asymptotic expression of eigenvalues and the exponential stability are readily obtained. The main results of [SIAM J. Control Optim., 36 (1998), pp. 1962-1986] are concluded as special case, and the additional conditions imposed there are removed.