The kinetics of irreversible dimer-dimer surface reactions of the type A(2)+B-2-->2AB with desorption of dimer B-2 has been investigated by means of Monte Carlo simulation. For a desorption probability (P) of B-2 equal to zero, a single discontinuous transition separating an A+vacancies saturated surface from a B+vacancies saturated surface is obtained at y(B2) = 0.5 (y(B2) is the partial pressure of B-2 in the gas phase). With the increase in P, a steady reactive state which is separated from the poisoned states by two continuous transitions is obtained for this system. The position of the transition points depends upon the value of P. For P equal to one, a single continuous transition at y(B2)=0.538 separates a poisoned state from a steady reactive state. The window width, which defines the steady reactive state, shows an exponential behavior with P. Preliminary studies have been under taken to determine the universality class of the system for different P values.