Let $n \ge 2$ be a natural number, $M$ a real $n \times n$ matrix, $s$ the sum of the entries of $M$ and $q$ the sum of their squares. With $α:= s/n$ and $β:= q/n$, Gasper's determinant bound says that $ |\det M| \le β^{n/2}$, and in case of $α^2 \ge β$: $$|\det M| \le |α| \left(\frac{nβ-α^2}{n-1}\right)^{\frac{n-1}2}$$ This article gives a corrected proof of Gasper's theorem and lists some more applications.