  The phase diagram of the Blume--Capel model on a semi--infinite simple cubic
lattice with a (100) free surface is studied in the pair approximation of the
cluster variation method. Six main topologies are found, of which two are new,
due to the occurrence of a first order surface transition in the phase with
ordered bulk, separating two phases with large and small surface order
parameters. The latter is a new phase and is studied in some detail, giving the
behaviour of the order parameter profiles in two typical cases. A comparison is
made with the results of a low temperature expansion, where these are
available, showing a great increase in accuracy with respect to the mean field
approximation.
