One of the most important and challenging problems in coding theory is to determine the optimal values of the parameters of a linear code and to explicitly construct codes with optimal parameters, or as close to the optimal values as possible. The class of quasi-twisted (QT) codes has been very promising in this regard. Over the past few decades various search algorithms to construct QT codes with better parameters have been employed. Most of these algorithms (such as ASR) start by joining constacyclic codes of smaller lengths to obtain QT codes of longer lengths. There has been an algorithm that works in the opposite way that constructs shorter QT codes from long constacyclic codes. We modified and generalized this algorithm and obtained new linear codes via its implementation. We also observe that the new algorithm is related to the ASR algorithm.