  The next-to-leading term of the renormalized stress-energy tensor of the
quantized massive field with an arbitrary curvature coupling in the spacetime
of the Schwarzschild black hole is constructed. It is achieved by functional
differentiation of the DeWitt-Schwinger effective action involving coincidence
limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients $a_{3}$ and
$a_{4}.$ The back reaction of the quantized field upon the Schwarzschild black
hole is briefly discussed.
