The stability domain is a feasible set for numerous optimization problems. D-decomposition technique is targeted to describe the stability domain in the parameter space for linear parameter-dependent systems. This technique is very simple and e_cient for robust stability analysis and design of low-order controllers. However, the geometry of the arising parameter space decomposition into root invariant regions has not been studied in detail it is an objective of the present paper. We estimate the number of root invariant regions and provide examples, where this number is attained.