The classical models of single neuron like Hodgkin-Huxley point neuron or leaky integrate and fire neuron assume the influence of postsynaptic potentials to last till the neuron fires. Vidybida (2008) in a refreshing departure has proposed models for binding neurons in which the trace of an input is remembered only for a finite fixed period of time after which it is forgotten. The binding neurons conform to the behaviour of real neurons and are applicable in constructing fast recurrent networks for computer modeling. This paper develops explicitly several useful results for a binding neuron like the firing time distribution and other statistical characteristics. We also discuss the applicability of the developed results in constructing a modified hourglass network model in which there are interconnected neurons with excitatory as well as inhibitory inputs. Limited simulation results of the hourglass network are presented.