In the last decade, many researchers have investigated the blind separation of sources and many algorithms have been proposed to solve this problem for the case of an instantaneous mixture (memoryless mixture) \cite{mansour-ieice-2000}. In general, high-order statistics (i.e., fourth order) are used. However, it has been shown that algorithms and criteria can be simplified by adding special assumptions \cite{jutten-intsymp-95}. In this paper, we outline the investigation of the separation of nonstationary signals using only second-order statistics. For the case of independent nonstationary (at least using second-order statistics) sources such speech signals where the power of the signals is considered time variant, we prove, using geometrical information, that the decorrelation of the output signals at any time leads to the separation of the independent sources. In other words, for these kinds of sources, any algorithm can separate the sources if at the convergence of this algorithm the covariance matrix of the output signals becomes a diagonal matrix at any time. Finally, some algorithms are proposed and the experimental results are discussed and shown. keywords: Decorrelation, Second-order Statistics, Whiteness, Blind separation of sources, Natural gradient, Kull-back divergence, Hadamard inequality, Jacobi Diagonalization, Cyclic Jacobi Diagonalization, Joint Diagonalization.