We propose a new recursive EM (REM) algorithm that can be used whenever the complete-data model associated to the observed data belongs to an exponential family of distributions. The main characteristic of our approach is to use a stochastic approximation algorithm to approximate the conditional expectation of the complete-data sufficient statistic rather than the unknown parameter itself. Compared to existing approaches, the new algorithm requires no analytical gradient or Hessian computation, it deals with parameter constraints straightforwardly and the resulting estimate can be shown to be Fisher-efficient in general settings. This approach is illustrated on the classic direction of arrival (DOA) model.