Let \({\mathcal S}_ n\) denote the space of all symmetric \(n\times n\) matrices and let \({\mathcal O}_ l\) be the subset of the regular matrices with index \(l\), \(0\leq l\leq n\). The author proves that the functions \(F_ l: {\mathcal S}_ n\to {\mathcal R}\) defined by \[ F_ l(X)= \begin{cases} |\text{det } X|\quad & \text{if }X\in {\mathcal O}_ l\\ 0 \quad & \text{otherwise}\end{cases} \] are quasiconvex. Some connections with the theory of gradient Young measures are also discussed.