Abstract: The local features in phase space and predictability are studied in this paper.It is illustrated that the local features in phace space have to be considered in determining predictability.The notions of local instability including the finit-time and local-time instability which determine the growth rate of the error are introduced and calculation methods are discussed in detail.The results from the calculation of the 3-component Lorenz model show that the local instability, correspondingly the growth rate of error, vary dramatically as trajetories evolve on the chaotic attractor.The region where the growth rate of error is small.is localized considerably and is separable from the region, where the growth rate of error is large.The local predictability depends on the region through which trajectories evolve.It is suggested that the local features are the main reasons why there is a great deal of case to case avariability of the predictive skill in operational forecasts.