  We introduce a new matroid width parameter based on the operation of matroid
amalgamation, which we call amalgam-width. The parameter is linearly related to
branch-width on finitely representable matroids (which is not possible for
branch-width). In particular, any property expressible in the monadic second
order logic can be decided in linear time for matroids with bounded
amalgam-width. We also prove that the Tutte polynomial can be computed in
polynomial time for matroids with bounded amalgam width.
