The pyrolysis and re-association of hydrogen sulphide is a key reaction in the Claus sulphur recovery process. In this paper, a new kinetic rate expression and its parameters for this reaction are derived under the conditions of the Claus reaction furnace. Experiments were performed with hydrogen sulphide using an isothermal, plug-flow reactor at temperatures between 850-115 degrees C and residence times of 50-1500 ms. The rate constants for the forward (pyrolysis or cracking of H2S) and reverse (re-association of H-2 and S-2) were derived through numerical simulation based on the collected experimental data. The form of the rate equation was determined to be r = A(f)e(-ef/RT) PH2SPS20.5 - A(r)e(-Er/RT)P(H2)P(S2), where A(f) and E-f, the forward parameters, are 5260 (+/- 260) mol/cm(3) s/atm(1.5) and 45.0 (+/- 0.3) kcal/mol, while the reverse parameters, A(r) and E-r, were 14 (+/- 1) mol/cm(3) s/atm(2) and 23.4(+/- 0.2) kcal/mol. The rate equation not only agrees with the experimental data within 15% but also agrees very well with published data. In addition, the rate expression properly predicts equilibrium compositions and is thermodynamically consistent.