Abstract Let Fn be the nth Fibonacci number. For 1 ≤ k ≤ m, let [ m k ] F = F m F m - 1 ⋯ F m - k + 1 F 1 ⋯ F k $$\left[ {\matrix{m \hfill \cr k \hfill \cr } } \right]_F = {{F_m F_{m - 1} \cdots F_{m - k + 1} } \over {F_1 \cdots F_k }}$$ be the corresponding Fibonomial coefficient. It is known that [ m k ] F $\left[ {\matrix{m \hfill \cr k \hfill \cr } } \right]_F $$$ is a Fibonacci number if and only if either k = 1 or m ∈ {k, k + 1}. In this note, we find all solutions of the Diophantine equation [ m k ] F ± 1 = F n $\left[ {\matrix{m \hfill \cr k \hfill \cr } } \right]_F \pm 1 = F_n $ .