Here, a new operational mode of an electromagnetic elliptical undulator, called leaf undulator, is proposed and studied. It can provide linearly polarized radiation at an arbitrary polarization direction depending on the magnitude and polarity of the horizontal and vertical magnetic fields. The polarization direction becomes 45 degrees when the horizontal and vertical magnetic fields are equal in strength. It is also able to switch the operational mode to purely circular or elliptical one. To lower the on-axis power density generated by undulators operating in linear mode, different designs have been presented in the past. Leaf undulator can suppress the on-axis power density by an order of magnitude compared to the so-called Knot and Figure-8 undulators, while maintaining comparable photon flux of the fundamental harmonic. Furthermore, it is possible to reach a lower fundamental energy under linear mode than by any other design using comparable magnetic field strengths.