We propose a method to smoothen a piecewise linear interpolation at a small number of nodes on a bounded interval. The method employs a sigmoidal type weight function having a property that clusters most points on the left side of the interval toward 0 and those on the right side toward 1. The proposed method results in a noninterpolatory approximation which is smooth over the whole interval. We provide an algorithm for implementing the presented smoothening method. To demonstrate usefulness of the presented method we introduce some numerical examples and investigate the results.