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Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments $$x^{\text{'}}\left(t\right)=A\left(t\right)x\left({\tau }_{11}\left(t\right)\right)+B\left(t\right)u\left({\tau }_{12}\left(t\right)\right)+q_1\left(t\right),u^{\text{'}}\left(t\right)=C\left(t\right)x\left({\tau }_{21}\left(t\right)\right)+D\left(t\right)u\left({\tau }_{22}\left(t\right)\right)+q_2\left(t\right),{\alpha }_{11}x\left(0\right)+{\alpha }_{12}u\left(0\right)=c_0,{\alpha }_{21}x\left(T\right)+{\alpha }_{22}u\left(T\right)=c_T$$ is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied.