Abstract: An improved method for independent component analysis based on the diagonalization of cumulant tensors is proposed. It is based on Comon's algorithm [Comon, 1994] but it takes third- and fourth-order cumulant tensors into account simultaneously. The underlying contrast function is also mathematically much simpler and has a more intuitive interpretation. It is therefore easier to optimize and approximate. A comparison with Comon's algorithm, JADE [Cardoso, 1993] and FastICA [Hyvärinen, 1999] on different data sets demonstrates its performance.