This paper analyzes in detail numerically a 40-Gb/s return-to-zero (RZ) transmission system over a transoceanic distance in a strongly dispersion managed line composed of standard single-mode fiber (SMF) and dispersion compensation fiber (DCF). We derived a periodically steady-state pulse (a DM soliton) in a DM line. Since the pulse width of a steady-state pulse is too broad for a 40 Gb/s system, the conventional in-line synchronous modulation technique cannot greatly improve the transmission quality. However, we found that the modified inline synchronous modulation technique, which is reported as the black-box optical regenerator, can effectively extend the transmission distance even in such a strongly DM line. We discuss the mechanism of the modified synchronous modulation technique with respect to a steady-state pulse in a transmission line, and show that a 40-Gb/s RZ signal can be transmitted over 20 000 km.