In this paper, we consider the problem of improving the stability properties of a class of second-order LTI systems by hybrid static output feedback. The improvement is measured in term of the stability index defined in the paper, and the systems under consideration are stabilizable with certain stability index by a single static output feedback. We show that an arbitrary desired stability index can be achieved for the system by designing a hybrid controller composed of two static output feedbacks and a conic switching law. An example is given to demonstrate the applicability of our result.