Rotational motions induced by earthquakes are expected to contain unique geophysical information not obtainable from translational motions, such as the distribution of slip velocity near the earthquake source. However their observations have not been performed as actively as those of translational motions, mainly because of technical difficulties. Rotational seismometers with sufficient resolution (better than 10-10 rad/sec/Hz1/2 over 0.1 mHz to 10 Hz) and reliability at reasonable cost are needed to establish broad observation networks for rotational seismology. To achieve this goal, we are developing a seismometer with a new design based on a proof mass levitated by a magnetic suspension that uses the flux pinning effect of a superconductor to make it freely rotatable without introducing unwanted parasitic resonances and other complexities. Prototype systems were built and tested to assess the feasibility of the technologies used in the new seismometer, and their advantages and capabilities have been successfully demonstrated. The design of the new seismometer together with the status of the development and future plans are presented in this article.