Cvetković, Rajković, and Ivković proved that the Hankel transform of the sequence of sums of two successive Catalan numbers is the sequence of Fibonacci numbers with odd indices. Later, Benjamin, Cameron, Quinn, and Yerger extended this result, and proved that if we remove one term from this sequence of sums, then the Hankel transform is the sequence of Fibonacci numbers with even indices. In this paper, we prove that the Catalan numbers are the unique nonnegative integer sequence satisfying this property.