This paper focuses on the covering mechanism in Learning Classifier System (LCS) which generates a new classifier (i.e., an if-then rule) when no classifier matches the input. We propose Local Covering, a niche-based rule generation method for XCS, to reduce the sensitivity of a hyperparameter that determines the generalization probability of initial rules. In Local Covering, the system looks up classifiers in the population and finds the closest match from the input. After that, the selected classifier is copied as the covering classifier and its condition is generalized to cover the input. To integrate the Local Covering method with XCS, XCS-LCPCI (XCS with Local Covering for Previously Covered Inputs) is proposed, which executes Local Covering only if the input has been previously covered by the covering processes. The experimental results with three different problems show that XCS-LCPCI successfully acquires the general classifiers with any of six different parameter settings, while the performance of the conventional XCS varies depending on the parameter settings.