The main aim of this short note is to obtain two sided bounding inequalities for the real argument Butzer-Flocke-Hauss complete Omega function improving and developing a recent result by Pogány and Srivastava [Some two-sided bounding inequalities for the Butzer-Flocke-Hauss Omega function, Math. Inequal. Appl. 10 (2007), 587-595]. The main tools are the ODE whose particular solution is the Omega function and the related Čaplygin type differential inequality.