Restarting automaton is a type of regulated rewriting system, introduced as a model for analysis by reduction. It is a linguistically motivated method for checking the correctness of a sentence. In this paper, we introduce a new definition of normal restarting automaton in which only one substring is removed using the DEL operation in a cycle. This DEL operation is applied to reverse the insertion operation in an insertion grammar. We use this 1-normal restarting automaton to solve the membership problem of insertion languages. Further, we introduce some interesting closure properties of 1-normal restarting automata. © 2017, Springer International Publishing AG.