The intermediate mass dileptons from the quark phase, secondary hadronic processes and background sources have been studied based on a relativistic hydrodynamic model. Due to the effect of the phase boundary on the evolution of the system the contribution from the quark phase is much more important than that from secondary processes and is even comparable with that from background sources. This leads to a spectrum without the obvious humps of the hadronic phase contribution and the yield increasing with the incident energy of colliding nuclei. It is shown that the enhancement of dileptons is a signature for the formation of the quark-gluon plasma.PACS: 25. 75. Dw, 12. 38. Mh, 24. 10. Nz