  A (positive definite and non-classic integral) quadratic form is called
strongly $s$-regular if it satisfies a strong regularity property on the number
of representations of squares of integers. In this article, we prove that for
any integer $k \ge 2$, there are only finitely many isometry classes of
strongly $s$-regular quadratic forms with rank $k$ if the minimum of the
nonzero squares that are represented by them is fixed.
