  A (positive definite and integral) quadratic form $f$ is called regular if it
represents all integers that are locally represented. It is known that there
are only finitely many regular ternary quadratic forms up to isometry. However,
there are infinitely many equivalence classes of regular quadratic forms of
rank $n$ for any integer $n$ greater than or equal to $4$. A regular quadratic
form $f$ is called new if there does not exist a proper subform $g$ of $f$ such
that the set of integers that are represented by $g$ is equal to the set of
integers that are represented by $f$. In this article, we prove that the rank
of any new regular quadratic form is bounded by an absolute constant.
