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Let $S$ be a semigroup, $z_0$ a fixed element in $S$ and $\sigma:S\longrightarrow S$ an involutive automorphism. We determine the complex-valuedsolutions of Kannappan-sine subtraction law$f(x\sigma(y)z_0)=f(x)g(y)-f(y)g(x),\; x,y \in S$. As an application we solvethe following variant of Kannappan-sine subtraction law viz.$f(x\sigma(y)z_0)=f(x)g(y)-f(y)g(x)+\lambda g(x\sigma(y)z_0) ,\; x,y \in S,$where $\lambda \in \mathbb{C}^{*}$. The continuous solutions on topologicalsemigroups are given and an example to illustrate the main results is alsogiven.

A Kannappan-sine subtraction law on semigroups