It is commonly acknowledged that a larger number of trade unions is associated with a higher level of employment. We demonstrate that this belief can be wrong, i.e. that the entry of trade unions can increase the number of unemployed workers. This result is stated in a multi-sector economy in which Cournotian trade unions incur no cost and have a nominal objective function. It is obtained when the labour demand function is sufficiently convex such that the trade-unions' actions become strong strategic complements. In addition, we show that this counterintuitive result is consistent with a wide range of parameter values under a CES technology.