  We deal with a novel approach to formulation of the relativistic dissipative
hydrodynamics by extending the so-called matching conditions widely used in the
literature. The form of the non-equilibrium entropy current can be determined
by requiring thermodynamical stability of the entropy current under extended
matching conditions. We derive equations of motion for the relativistic
dissipative fluid based on the Eckart theory and show that linearized equations
obtained from them are stable against small perturbations. It is also shown
that the required fluid stability conditions are related to the causality of
the model.
