We consider positional numeration system with negative base −β, as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when β is a quadratic Pisot number. We study a class of roots β>1 of polynomials x2−mx−n, m≥n≥1, and show that in this case the set Fin(−β) of finite (−β)-expansions is closed under addition, although it is not closed under subtraction. A particular example is β=τ=12(1+5–√), the golden ratio. For such β, we determine the exact bound on the number of fractional digits appearing in arithmetical operations. We also show that the set of (−τ)-integers coincides on the positive half-line with the set of (τ2)-integers.