Summary: Our goal of this paper is to find a construction of all \(\ell\)-quasi-cyclic self-dual codes over a finite field \(\mathbb{F}_q\) of length \(m\ell\) for every positive even integer \(\ell\). In this paper, we study the case where \(x^m -1\) has an arbitrary number of irreducible factors in \(\mathbb{F}_q [x]\); in the previous studies, only some special cases where \(x^m -1\) has exactly two or three irreducible factors in \(\mathbb{F}_q [x]\), were studied. Firstly, the binary code case is completed: for any even positive integer \(\ell\), every binary \(\ell\)-quasi-cyclic self-dual code can be obtained by our construction. Secondly, we work on the \(q\)-ary code cases for an odd prime power \(q\). We find an explicit method for construction of all \(\ell\)-quasi-cyclic self-dual codes over \(\mathbb{F}_q\) of length \(m\ell\) for any even positive integer \(\ell\), where we require that \(q \equiv 1 \pmod{4}\) if the index \(\ell \geq 6\). By implementation of our method, we obtain a new optimal binary self-dual code \([172, 86, 24]\), which is also a quasi-cyclic code of index 4.