In a recent paper, Isao Kiuchi and Naoki Yanagisawa studied the even power moments of the error term in the approximate functional equation for $\zeta(s)$ . They got a mean value formula with an error term $O(T^{1/2-k\sigma})$ , and then they conjecture that this term could be replaced by $E_{k,\sigma}T^{1/2-k\sigma}(1+o(1))$ with constant $E_{k,\sigma}$ depending on $k$ and $\sigma$ . In this paper, we disprove this conjecture by showing that the error term should be $f(T)T^{1/2-k\sigma}+o(T^{1/2-k\sigma})$ with $f(T)$ oscillating.