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The conformally invariant symmetric traceless field $A$ is considered onconformally flat Einstein space-time. If $d=4$ this field possess a scalargauge invariance. In that case, we provide a conformally invariant gaugecondition which generalizes in a simple manner, on those space-time, theEastwood-Singer gauge condition. A field strength $F$ is built upon thepotential $A$, its properties are worked out in details, giving raise to a newset of conformally invariant equations.

A conformally invariant gauge fixing equation and a field strength for  the symmetric traceless field over four dimensional conformally flat Einstein  spacetimes