  A Heffter array $H(n;k)$ is an $n\times n$ matrix such that each row and
column contains $k$ filled cells, each row and column sum is divisible by
$2nk+1$ and either $x$ or $-x$ appears in the array for each integer $1\leq
x\leq nk$. Heffter arrays are useful for embedding the graph $K_{2nk+1}$ on an
orientable surface. An integer Heffter array is one in which each row and
column sum is $0$. Necessary and sufficient conditions (on $n$ and $k$) for the
existence of an integer Heffter array $H(n;k)$ were verified by Archdeacon,
Dinitz, Donovan and Yaz\i c\i \ (2015) and Dinitz and Wanless (2017). In this
paper we consider square Heffter arrays that are not necessarily integer. We
show that such Heffter arrays exist whenever $3\leq k<n$.
