Let χ be a virtual (generalized) character of a finite group G and be the image of χ on The pair is said to be sharp of type L or L-sharp if If the principal character of G is not an irreducible constituent of χ, the pair is called normalized. In this paper, we first provide some counterexamples to a conjecture that was proposed by Cameron and Kiyota in 1988. This conjecture states that if is L-sharp and then the inner product is uniquely determined by L. We then prove that this conjecture is true in the case that is normalized, χ is a character of G, and L contains at least an irrational value.