Beckmann rearrangements of oximes to lactams often require harsh conditions and/or the use of large amounts of acid catalyst. To reduce the amount of Brønsted acid required, and to avoid the formation of a large amount of undesirable byproducts under mild reaction conditions, a low environmental load process was developed. Beckmann rearrangements of cyclohexanone oxime and cyclooctanone oxime were achieved using a combination of a Brønsted acid and cobalt tetrafluoroborate hexahydrate. Various Brønsted acid catalysts (10 -20 mol%) were used to obtain the corresponding lactams in high yields at 80˚C.