The state of North Dakota, through its several departments and agencies, is hereby authorized and empowered to exchange tracts, sections, and parcels of land located within the diminished borders of Fort Berthold reservation belonging to the state of North Dakota and not a part of the original grant of lands to the state provided for in the Enabling Act, for lands of like character and value belonging to the United States government located outside of the diminished borders of said Fort Berthold reservation. Such exchange is subject to the approval of the proper department of the federal government, and such lands must be appraised as provided by law in the case of sale of real property owned by the state. The state also may execute and deliver proper conveyances of such land in the manner and form provided by law, without the necessity of complying with any statute requiring the giving of notice of exchange or competitive bidding, and may accept in return therefor a proper instrument of conveyance to the state of North Dakota of the land for which such lands are exchanged.