The problem of separating blindly independent sources from a convolutive mixture cannot be addressed in its widest generality without resorting to statistics of order higher than two. The core of the problem is in fact to identify the paraunitary part of the mixture, which is addressed in this paper. With this goal, a family of statistical contrast is first defined. Then it is shown that the problem reduces to a Partial Approximate Joint Diagonalization (PAJOD) of several cumulant matrices. Then, a numerical algorithm is devised, which works block-wise, and sweeps all the output pairs. Computer simulations show the good behavior of the algorithm in terms of Symbol Error Rates, even on very short data blocks.