A novel orthoborate, NaMgBO3, has been successfully synthesized by a standard solid-state reaction, and the crystal structure has been determined from powder X-ray diffraction data. It crystallizes in the monoclinic space group C2/c with lattice parameters a = 5.01313(6) angstrom, b = 8.8007(1) angstrom, c = 5.52831(7) angstrom, and beta = 99.6962(6)degrees. Isolated [BO3](3-) anionic groups, which are the fundamental building units, are distributed perfectly parallel to each other. It is a typical structure of big birefringent crystals. The overall structure is similar to that of NaSrBO3, which crystallizes in P2(1)/c. The correlation between these two structures is discussed. The Mg atoms in NaMgBO3 are used instead of the position of Na in NaSrBO3, while the Na atoms occupy the position of Sr. Then the directions of the BO3 triangles are changed to balance the bond valence, which leads to a higher symmetry. They are the first pair of alkali-alkaline earth orthoborates with close space groups by exchange of the cation positions.