The exponential stability of the trivial solution to the state-dependent delay differential equation \[ \dot x (t) =a(t)x(t-\tau (t,x(t))) \] is investigated. It is shown that, under some conditions, this state-dependent equation is exponentially stable, if the trivial solution to \[ \dot y (t)=a(t)y(t-\tau (t,0)) \] is exponentially stable. Assuming the existence of bounded partial derivatives of the delay function, the reverse statement is proved.