Summary: Let \(\mathcal{T}=\{T_1,T_2,\dots,T_k\}\) be a set of \(k\geq 2\) spanning trees in a graph \(G\). The \(k\) spanning trees are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices \(x\) and \(y\) in any two trees have neither vertex nor edge in common except for \(x\) and \(y\). Particularly, \(\mathcal{T}\) is called a dual-CIST provided \(k=2\). For data transmission applications in reliable networks, the existence of a dual-CIST can provide a configuration of fault-tolerant routing called protection routing. This paper investigates the problem of constructing a dual-CIST in the \(n\)-dimensional hierarchical folded cubic network \(HFQ_n\). The network is a two-level network using folded hypercube \(FQ_n\) as clusters to reduce the diameter, hardware overhead and improve the fault tolerance ability. We propose a recursive algorithm to construct a dual-CIST of \(HFQ_n\) in \(\mathcal{O}(2^{2 n})\) time for \(n\geq 2\), where the time required is the same scale as the number of vertices of \(HFQ_n\). Also, the diameter of each constructed CIST is \(4n+1\).