An explicit unconditionally stable algorithm for hybrid tests, which is developed from the traditional HHT-α algorithm, is proposed. The unconditional stability is first proven by the spectral radius method for a linear system. If the value of α is selected within [-0.5, 0], then the algorithm is shown to be unconditionally stable. Next, the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system. The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening. To improve the stability of the proposed method, the structure stiffness is then identified and updated. Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.