Although the family methods with unconditional stability and numerical dissipation have been developed for structural dynamics they all are implicit methods and thus an iterative procedure is generally involved for each time step. In this work, a new family method is proposed. It involves no nonlinear iterations in addition to unconditional stability and favorable numerical dissipation, which can be continuously controlled. In particular, it can have a zero damping ratio. The most important improvement of this family method is that it involves no nonlinear iterations for each time step and thus it can save many computationally efforts when compared to the currently available dissipative implicit integration methods.