Accurate and stable stiffness control is required for robots that need to interact safely with human or the environment. Accurate stiffness control can be achieved using a series elastic actuators (SEA). An SEA includes an elastic spring in series with an actuator to provide more accurate force control than conventional rigid actuators. Although impedance and admittance controllers have both been developed for series elastic actuators to render virtual stiffness, the stable virtual stiffness is still largely limited by the stiffness of the elastic spring in the SEA. Increasing the stiffness of the spring can allow a larger range of stable virtual stiffness. However, the accuracy of the stiffness control would be compromised. Adding a virtual damper can also improve the stability, but the stability range would highly depend on the environmental parameters. To overcome the limitations, this paper proposes a novel control strategy such that the stable range of the virtual stiffness does not depend on the spring stiffness and the environmental parameters. Both impedance and admittance controllers will be modified based on this new control strategy. The stability analysis of the modified controllers will show that the virtual stiffness can be arbitrarily selected and is unrelated to the spring stiffness and environmental parameters. It is expected that the new control strategy can be used for SEAs when wide-range and accurate virtual stiffness is required.