In this paper, the spontaneous emission by two identical two-level atoms, separated a distance apart, both initially excited is considered. Using the method outlined by Ujihara and Dung [Phys. Rev. A 66 (2002) 053871, the analytical expression for the time dependent atomic-state amplitude is presented. On the basis of this analysis of atomic motion, the near-field intensity of two atoms spontaneous emission and its transition to the far field are investigated. Within fourth-order perturbation, the intensity has contributions from the states where a single or two photons exist. These states each result from different emission sequences that can show quantum interference. Our results are in consistency with the `super-radiance' feature predicted by Dicke. The spatial interference fringe at a certain time in the spontaneous emission, though numerically small, the quantum interference effect in the initially excited two-atom spontaneous emission are evidently existing. (C) 2004 Elsevier B.V. All rights reserved.