Adaptive software testing is the counterpart of adaptive control in software testing. It means that software testing strategy should be adjusted online by using the testing data collected during software testing as our understanding of the software under test improves. Previous studies on adaptive testing rely on a simplified Controlled Markov Chain (CMC) model for software testing which employs several unrealistic assumptions. In this paper we propose a new adaptive software testing approach in the context of an improved CMC model which aims to eliminate such threats to validity. A new set of basic assumptions on the software testing process is proposed and several unrealistic assumptions are replaced by more common situations in real life software testing. The methodology of a new adaptive testing strategy is also developed and implemented. Experimental data are collected to demonstrate the effectiveness of the new methodology.