Recently, Cenzato et al.\ proposed a new text index, called the \emph{suffixient array}, which is a subset of the suffix array and supports locating a single pattern occurrence or finding its maximal exact matches (MEMs), assuming random access to the input text $T[1..n]$ is available. They show that, given the suffix array, the longest common prefix array, and the Burrows--Wheeler transform (BWT) of the reverse of $T[1..n]$ over an alphabet $\{1,\ldots,σ\}$, a suffixient array can be constructed in linear time. However, their construction algorithms require multiple scans of these arrays. When restricted to a single pass over the arrays, they present an alternative construction algorithm running in $O(n + \overline{r} \log σ)$ time, where $\overline{r}$ is the number of runs in the BWT of the reversed text. In this paper, we present a new one-pass algorithm that constructs a suffixient array in linear time under the standard RAM model.