Since the safety of seismically-isolated buildings during earthquakes depends mainly on the largedeformation stability of the isolation devices, it is necessary to either provide large isolator deformation capacity or to reduce seismic response deformation to ensure enhanced building safety. From the viewpoint of earthquake demand, it must be recognized that, the isolator response deformation may exceed the allowable capacity when the isolation system resonates with strong, near-source earthquake ground motions. This paper first establishes the problem of the damping capacity of conventional isolation systems that a system with strong restoration spring causes large elastic strain energy to accumulate in largely deformed isolators. Then, a new hysteresis behavior is proposed to reduce the strain energy developed in isolators. Based on studies of the fundamental characteristics of the proposed hysteresis behavior, this paper proposes a new isolation system concept called “Seismic Isolation with No Strain Energy (NSE)” which does not result in resonance because it eliminates the strain energy stored in deformed isolators, even if the period of the isolation system coincides with predominant period of the input ground motions. The superior performance of NSE Seismic Isolation is confirmed by the results of dynamic response analyses for strong, near-source earthquake ground motions.