  Surjective isometries between unital C*-algebras were classified in 1951 by
Kadison. In 1972 Paterson and Sinclair handled the nonunital case by assuming
Kadison's theorem and supplying some supplementary lemmas. Here we combine an
observation of Paterson and Sinclair with variations on the methods of Yeadon
and the author, producing a fundamentally new proof of the structure of
surjective isometries between (nonunital) C*-algebras. In the final section we
indicate how our techniques may be applied to classify surjective isometries of
noncommutative Lp spaces, extending some recent results of the author to 0 < p
leq 1.
