A new approach has been developed for the synthesis and design of heat exchanger networks featuring streams with unequal film heat-transfer coefficients. The methodology couples the new block method proposed by Zhu et al. with the concept of individual stream DELTAT contributions as introduced by Rev and Fonyo. It generates improved solutions to problems involving unequal film coefficients compared with currently available methods. In this new approach, different stream structures can be screened and compared prior to detailed design. This enables the designer to determine an attractive stream structure featuring low area for subsequent analysis. Potentially good matches are readily identified and topology traps can be effectively avoided. As a consequence, good initial designs are degenerated and available for subsequent cost optimization using nonlinear programming. The likelihood of identifying a globally optimal design is substantially increased.