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We present a new method for computing complete one-loop amplitudes, including their rational parts, in non-supersymmetric gauge theory. This method merges the unitarity method with on-shell recursion relations. It systematizes a unitarity-factorization bootstrap approach previously applied by the authors to the one-loop amplitudes required for next-to-leading order QCD corrections to the processes e^+e^- -> Z,\gamma^* -> 4 jets and pp -> W + 2 jets. We illustrate the method by reproducing the one-loop color-ordered five-gluon helicity amplitudes in QCD that interfere with the tree amplitude, namely A_{5;1}(1^-,2^-,3^+,4^+,5^+) and A_{5;1}(1^-,2^+,3^-,4^+,5^+). Then we describe the construction of the six- and seven-gluon amplitudes with two adjacent negative-helicity gluons, A_{6;1}(1^-,2^-,3^+,4^+,5^+,6^+) and A_{7;1}(1^-,2^-,3^+,4^+,5^+,6^+,7^+), which uses the previously-computed logarithmic parts of the amplitudes as input. We present a compact expression for the six-gluon amplitude. No loop integrals are required to obtain the rational parts.