The authors of this manuscript propose a new formulation of stable first-order relativistic dissipative hydrodynamics in the particle frame, also called the Eckart frame. The new hydrodynamic equation is derived from the relativistic Boltzmann equation by means of the renormalization-group method. Older versions of relativistic hydrodynamics in the Eckart frame imposed the condition that the energy density in the comoving frame does not have a dissipative component (of course, the energy flow has such a contribution describing heat flow), the new equation posits that the dissipative energy-momentum tensor is traceless. The authors show that their constraint is compatible with the Boltzmann equation, but the old constraint is not. They also show that the new equation, in contrast to the traditional formulation, assures the stability of the equilibrium state under time evolution.