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

Next-to-leading term of the renormalized stress-energy tensor of the quantized massive scalar field in Schwarzschild spacetime. The back reaction