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The nonlocal Darboux transformation of the two - dimensional stationarySchr\"odinger equation is considered and its relation to the Moutardtransformation is established. It is shown that a special case of the nonlocalDarboux transformation provides the Moutard transformation. New examples ofsolvable two - dimensional stationary Schr\"odinger operators with smoothpotentials are obtained as an application of the nonlocal Darbouxtransformation.

The nonlocal Darboux transformation of the 2D stationary Schr\"odinger equation and its relation to the Moutard transformation