A detailed study of the relation between diffraction points of various rhombohedral types and the type 6H of silicon carbide has been made, using the reciprocal lattice method. It was shown that there occur twelve possible relations. A method was proposed for determining the number of the close hexagonal packed layers in unit cell from the relations derived and the numbers of point between two Laue points of the type 6H. By using the method proposed, numerous SiC single crystals prepared in our laboratory were analysed and two new modifications of α-SiC 417R and 453R were found. These two new types are coalescent with the most common type 6H. The space group of the new types is R3m (C3v5). The unit cell dimensions in the hexagonal system for 417R and 453R are as follows respectively: 417R:αH=3.0806?,c=1050.7?,Z=417; 453R:αH=3.0806?,c=1141.4?,Z=453 or, in the rhombohedral unit cell: 417R:αR=350.4?,α=30.4′,Z=139; 453R:αR=380.6?,α=27.8′,Z=151.