Conventional blind signal separation algorithms do not adopt any asymmetric information of the input sources, thus the convergence point of a single output is always unpredictable. However, in most of the applications, we are usually interested in only one or two of the source signals and prior information is almost always available. In this paper, a principal independent component analysis (PICA) concept is proposed.We try to extract the objective independent component directly without separating all the signals. A cumulant-based globally convergent algorithm is presented and simulation results are given to show the hopeful applicability of the PICA ideas.