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The paper presents a new and unifying view of multiple-input multiple-output instantaneous blind identification based on the main assumptions that the cross-cumulant functions of the source signals of some arbitrary fixed order vanish for all time tuples and that the source auto-cumulant functions of the same order are linearly independent. Hence, the time structure of the signals is exploited. The paper provides new insight into the algebraic and geometric structure of the problem, which is crucial for the development of solutions. The presented viewpoint is unifying in two senses. Firstly, the developed theory is general with respect to the considered order of the cumulants. Secondly, all types of statistical variability in the data, for example, the nonstationarity and the nonwhiteness, are incorporated into the problem in a unified manner.