To provide an in-depth understanding on the complexation mechanism of protein and polyelectrolyte, a heating-cooling-reheating protocol was employed to study the unfolding and refolding behaviors of a model protein, lysozyme, in the presence of the negatively charged polyelectrolyte, sodium poly(styrenesulfonate) (PSS). It was found that with elevated PSS concentration, a new state (state I) was first formed via a "two-state" conversion process, and this state could further convert to a completely unfolded state (state II) via the "non-two-state" conversion. This "non-two-state" conversion process occurs without the coexistence of the two states I and II, but involves the formation of various intermediate unfolded protein structures. Different from the pure lysozyme that exhibited refolding upon cooling from its heat-denatured state, lysozyme in state I could undergo unfolding upon heating but no refolding upon cooling, while lysozyme in state II did not undergo unfolding or refolding upon thermal treatments. Besides, the effects of ionic strength and the molecular weight of the polyelectrolyte on the unfolding and refolding behaviors of lysozyme were also investigated. The present work provides a better understanding on the principles governing the protein-polyelectrolyte interactions and may have implications for the fabrication of biocolloids and biofilms.