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The recent breakthroughs in numerical relativity have made it possible to generate the gravitational wave signals coming from binary black hole systems. The waveforms are are extracted using the Newman-Penrose formalism and in particular the Weyl scalar Psi4. In order for Psi4 to contain the physical information on the gravitational wave signal, the tetrad chosen for its calculation should converge to the Kinnersley tetrad in the limit of single black hole space-time. Here we present a compact expression for Psi4 that automatically enforces this condition, making it a useful and simple to implement formula for wave extraction in numerical relativity.
