Correlation based Minimum Spanning Tree (MST) networks are instrumental in capturing the basic workings of a system andhave been accepted for use in the analysis of stock and currency exchange markets. Research in network analysis of financialmarkets shows that although correlations underlying MST networks capture essential information, they do not faithfully capturedynamic behavior embedded in the time series data of financial systems. We present a new Phase Synchronization (PS) basedmethod for establishing correlations between nonlinear time series data, prior to constructing the MST. In this method, timeseries data generated by each entity in a system is transformed to a recurrence plot and the recurrence plots are furthertransformed to trajectories in phase space. For each pair of trajectories, phase synchronization (PS) is quantified based on the degree of phase locking observed. Distances for the MST are then computed as a function of the PS between each entity pair. We demonstrate the method using Thailand Baht exchange rates with 82 countries from 2004 to 2012. We further analyze and compare networks constructed using the PS method (PSMST) and the existing crosscorrelation method (CCMST), to study the differences in market dynamics captured by these methods.