The transition from the traditional cylindrical discharge geometry to the coaxial one (where the discharge plasma is located in a gap between two coaxially placed cylindrical tubes) has been theoretically investigated for the positive column of an electronegative middle pressure glow discharge in the mixture of chlorine and inert gases. Here a new electron’s loss mechanism appears, i.e. the electron’s diffusional outgoing onto the inner wall. The discharge existence was proved to be only made possible by sufficient increasing of the ionization frequency and hence the electron temperature as well. The elevation of the electron temperature would cause a growth of the specific power of discharge ultraviolet radiation. The analytical expressions for estimating the electron temperature of the discharge plasma in the coaxial geometry were derived.