We present a modification to the AprioriBL algorithm, which is an extension to a well-known Association Mining algorithm, Apriori. AprioriBL targets the borderline cases of frequent itemsets; however, it performs poorly. Our new algorithm, AprioriBLT, considers only the borderline cases for generating itemsets. This increases performance at the cost of accuracy. A comparison is made between AprioriBL and AprioriBLT, and the efficacy of AprioriBLT is discussed.