A merit function based on short length linear predictability of signal in an objective probabilistic algorithm is defined and used for blind source separation (BSS) of linear mixtures of signals. In BSS literatures, it has been conjectured that linear mixture of statistically independent source signals will result in a set of signals which each of them has less predictability than (or equal to) that of any of component source signals. We have used this property to extract source signals by finding an un-mixing matrix that maximizes the proposed merit function of predictability for each recovered signal. This method which is called Probabilistic Short-length Linear Predictability BSS (PSLP-BSS), its performance has been driven with many tests performed with mixtures of different kinds (speech, audio, image, constructed mathematical signals like saw tooth and sinusoidal). In all cases, correlation between each of source signals and each of extracted signals shows near-perfect performance of the method. The proposed BSS doesnt require any assumption regarding the probability density function of source signals. It has been demonstrated that PSLP-BSS can separate signal mixtures in which each mixture is a linear combination of source signals with gaussian, super-gaussian and sub-gaussian probability density functions. However, the method is adapted to temporal structure of recovered signals. Since, the un-mixing matrix that is concluded by proposed merit function can be obtained as the solution to a generalized eigenvalue routine, signals can be extracted simultaneously using the fast eigen value.