Is there a non-contradictory non-trivial axiomatic system in which Gödel's theorem is undecidable? Gödel's Incompleteness Theorem states that in any non-contradictory non-trivial axiomatic system there are certain statements or theorems whom cannot be proved in that system, For example in ZFC, assuming it is non-contradictory, there is the famed Continuum Hypothesis and Whitehead's problem. My question is, is there any such system (but different from ZFC) in which Gödel's Incompleteness Theorem itself is an unprovable statement?

Robinson arithmetic is non-trivial enough that the incompleteness theorem applies to it, but as far as I know not strong enough to prove the incompleteness theorem itself.