Nonvolatile memories have attracted a lot of interest because they retain the data when the power is interrupted. Smaller size and improved performance of nonvolatile memories are pursued both for basic research and applications. In this work, a molecular wire made of seamless junctions between semiconducting single-walled carbon nanotubes (SWNT) and partially unzipped segments of the SWNTs are reported. This novel nanostructure is demonstrated to be a nonvolatile memory, which works at room temperature under atmospheric conditions. The characteristics of the device are measured with a four-terminal configuration and a non-local voltage (Vnon-local) is used as the storage signal. An electrical hysteresis of Vnon-local is observed, wherein two states with different Vnon-local can be switched by the application of an electric field through an insulating gate device structure, exhibiting nonvolatile characteristics. Vnon-local can be modulated with external magnetic fields and the mechanism of the electrical hysteresis is attributed to the magnetic moments at the partially unzipped SWNT. The smaller size of SWNT and high working temperature may lead to the development of molecular nanomagnets as nonvolatile memory devices for practical applications.