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. However, this increase in the amount of data may also increase the likelihood of incorrectly linked records among databases. 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 paper, we improve on a Markov Chain based Monte Carlo simulation approach (MaCSim) for assessing a linking method. MaCSim utilizes two linked files that have been previously linked on similar types of data to create an agreement matrix and then simulates the matrix using a proposed algorithm developed to generate re-sampled versions of the agreement matrix. A defined linking method is used in each simulation to link the files and the accuracy of the linking method is assessed. The improvement proposed here involves calculation of a similarity weight for every linking variable value for each record pair, which allows partial agreement of the linking variable values. A threshold is calculated for every linking variable based on adjustable parameter "tolerance" for that variable. To assess the accuracy of linking method, correctly linked proportions are investigated for each record. The extended MaCSim approach is illustrated using a synthetic dataset provided by the Australian Bureau of Statistics (ABS) based on realistic data settings. Test results show higher accuracy of the assessment of linkages.