Record linkage is the process of bringing together the same entity from overlapping data sources while removing duplicates. Huge amounts of data are now being collected by public or private organizations as well as by researchers and individuals. Linking and analysing relevant information from this massive data reservoir can provide new insights into society. It has become increasingly important to have effective and efficient methods for linking data from different sources. Therefore, it becomes necessary to assess the ability of a linking method to achieve high accuracy or to compare between methods with respect to accuracy. In this article, we improve on a Markov Chain based Monte Carlo simulation approach (