A set of finitary operations on a finite set A is called a clone on A if it contains all projections and is closed under superposition. In his paper [Rozpr. Česk. Akad. Věd., Řada Mat. Přír. Věd. 80, No.4, 3-93 (1970; Zbl 0199.302)], \textit{I. G. Rosenberg} classified the maximal clones. In the paper [Z. Math. Logik Grundl. Math. 24, 79-96 (1978; Zbl 0401.03008)] by \textit{D. Lau}, it has been shown that for \(| A| \leq 7\) every maximal clone on A is finitely generated. In the present paper, the author studies a maximal clone on a set of eight elements and proves, that this clone - which consists of all finitary operations preserving a certain partial order - is not finitely generated. Since it is already known that all other maximal clones on an eight element set are finitely generated, this result settles the case \(| A| =8\).