The authors analysis the Krylov-type subspace method for a reduction of a linear dynamical system with many inputs and construct the tangential modification of this method. The method consists in the generation of the sequence of the interpolation poles \( s_{i}\) and tangential directions \( d_{i}\) by maximizing the residual norm. Also, this method is applied for the matrix \( A \) stemming from the discretization of the operator \[ L(u) = ( e^{-xy}u_{x})_{x}+ ( -e^{xy}u_{y})_{y} \] and the comparison with other methods is shown. The content of the article is exposed in an unsuccessful manner.