It is pointed out that the counter-rotating terms play an important role in the superradiance of the first kind, in which the atomic system is initially in an uncorrelated state with maximal dipole moment. If the counter-rotating terms are added to the master equation for the Dicke model derived by Agarwal and Bonifacioet al., the numerical solutions for the atomic-population inversion and radiation rate show strong damped oscillations (damped recurrence effects) in their time behaviour. A new limiting relation for the cut-off frequency, which depends on the number of atoms, is also obtained for the treated model.