A novel unitary optical mode converter was proposed, which can transform Hermite-Gaussian beams with the same Rayleigh range and waist position into Laguerre-Gaussian beams. Being unitary and having only two reflecting faces, the mode converter was easily adjusted and had very small reflecting loss. In view of the Hertmite-Gaussian beams with different Rayleigh range and waist position, a waist adjuster was proposed. Such Hertmite-Gaussian beams can also be transformed into Laguerre-Gaussian beams by combining the adjuster and the converter.