By applying a unified real space renormalization group (URG) mapping method, we study the one-dimensional spin-1/2 Ising model with a transverse field (ITF). Unlike the other real space renormalization group methods, the URG method describes the properties of the model at both zero and finite temperatures in a unified way. The results obtained are in good agreement with that obtained by other methods. Application of the URG method to other quantum spin systems is discussed.