  A new recursive procedure to compute the Zassenhaus formula up to high order
is presented, providing each exponent in the factorization directly as a linear
combination of independent commutators and thus containing the minimum number
of terms. The recursion can be easily implemented in a symbolic algebra package
and requires much less computational effort, both in time and memory resources,
than previous algorithms. In addition, by bounding appropriately each term in
the recursion, it is possible to get a larger convergence domain of the
Zassenhaus formula when it is formulated in a Banach algebra.
