The problem of blind separation of overdetermined mixtures of sources, that is, with fewer sources than (or as many sources as) sensors, is addressed in this paper. A new method, named ICAR (Independent Component Analysis using Redundancies in the quadricovariance), is proposed in order to process complex data. This method, without any whitening operation, only exploits some redundancies of a particular quadricovariance matrix of the data. Computer simulations demonstrate that ICAR offers in general good results and even outperforms classical methods in several situations: ICAR ~(i) succeeds in separating sources with low signal to noise ratios, ~(ii) does not require sources with different SO or/and FO spectral densities, ~(iii) is asymptotically not affected by the presence of a Gaussian noise with unknown spatial correlation, (iv) is not sensitive to an over estimation of the number of sources.