On the Weak Point of the Stronger Uncertainty Relation

We analyze the uncertainty relation for the sum of variances, which is called in some papers, the stronger uncertainty relation for all incompatible observables. We show that this uncertainty relation for the sum of variances of the observables $A$ and $B$ calculated for the eigenstate of one of these observables, (say of $B$), contrary to the suggestions presented in some papers, leads to the same results as the Heisenberg--Robertson uncertainty relation, that it does not give any bounds on the variance of $A$.