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According to the theory of relativity and causality, a special type ofcorrelation beyond quantum mechanics is possible in principle under the name of{\it non-local box}. The concept has been introduced from the principle ofnon-locality which satisfies relativistic causality. In this paper, we showthat a correlation leading to the non-local box is possible to be derivedconsistently if we release the one of major axioms in quantum mechanics, {\itBorn's rule}. This allows us to obtain a theory which in one end of thespectrum agrees with the classical probability and in the other end, agreeswith the theory of non-local causality. At the same time, we argue that thecorrelation lies in a space with special mathematical constraints such that aphysical realization of the correlation through a probability measure is notpossible in one direction of its limit and is possible in the other limit.

Consistent theory for causal non-locality beyond Born's rule