This paper considers the joint estimation of the parameters of a first-order fractional autoregressive model by constructing an initial estimator with convergence speed lower than √ n and singular asymptotic joint distribution. The one-step procedure is then used in order to obtain an asymptoticallyefficient estimator. This estimator is computed faster than the maximum likelihood or Whittle estimator and therefore allows for faster inference on large samples. The paper illustrates the performance of this method on finite-size samples via Monte Carlo simulations.