In order to decrease remarkably the computation time and storage used in the direct integration method without the loss of accuracy, authors suggest a new transient analysis algorithm. This algorithm is derived from the combination of three techniques, that is, the transfer technique of the transfer stiffness coefficient method, the modeling technique of the finite element method, and the numerical integration technique of the Newmark method. In this paper, the transient analysis algorithm of a frame structure is formulated by the proposed method. The accuracy and computation efficiency of the proposed method are demonstrated through the comparing with the computation results by the direct integration method for three computation models under various excitations.