One of the most important topics in the study of the dynamics of open quantum systems is the information exchange between system and environment. Based on the features of back-flow information from an environment to a system, an approach is provided to detect non-Markovianity for unital dynamical maps. The method takes advantage of non-contraction property of the von Neumann entropy under completely positive and trace-preserving unital maps. Accordingly, for the dynamics of a single qubit as an open quantum system, the sign of the time derivative of the density matrix eigenvalues of the system determines the non-Markovianity of unital quantum dynamical maps. The main characteristics of the measure are to make the corresponding calculations and optimization procedure simpler.