In this paper we have studied the spatiotemporal behaviour of threshold coupled bistable chaotic maps. We have shown the existence of various cycles of the single map with the variation of threshold value for fixed relaxation time. The effects of variation of relaxation time on the network of threshold coupled maps are presented for different threshold values. Excess propagation through open boundaries is calculated numerically. For a network of three threshold coupled maps, the propagation of excess through open boundaries is calculated analytically. The condition for the existence of the steady state profile of the excess is calculated. The effects of random coupling on spatiotemporal synchronization of the network of threshold coupled maps are investigated. The key observation is that threshold coupling provides an annihilation method of the coexisting chaotic attractors of the local map and stabilizes it to some fixed point or periodic attractor. © 2014 The Royal Swedish Academy of Sciences.