This paper proves the following result: Let \(q\) be the square of an odd prime power and let \(m \geq q\). Then \(PSp(2m,q)\) is the Galois group of a regular Galois extension of \(\mathbb{Q}(x)\). The proof is an outgrowth of the idea of rigidity, but the Nielsen classes in this instance are not rigid. The methods used in this paper may well be able to be used to produce additional examples of simple groups which are Galois groups of regular extensions of \(\mathbb{Q}(x)\).