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Given 
$\alpha \gt 0$ and an integer 
$\ell \geq 5$, we prove that every sufficiently large 
$3$-uniform hypergraph 
$H$ on 
$n$ vertices in which every two vertices are contained in at least 
$\alpha n$ edges contains a copy of 
$C_\ell ^{-}$, a tight cycle on 
$\ell$ vertices minus one edge. This improves a previous result by Balogh, Clemen, and Lidický.
