Summary: We present version 4.0 of the symbolic manipulation system Form. The most important new features are manipulation of rational polynomials and the factorization of expressions. Many other new functions and commands are also added; some of them are very general, while others are designed for building specific high level packages, such as one for Gröbner bases. New is also the checkpoint facility, that allows for periodic backups during long calculations. Finally, Form 4.0 has become available as open source under the GNU General Public License version 3.