  We formulate a new error-disturbance relation, which is free from explicit
dependence upon variances in observables. This error-disturbance relation shows
improvement over the one provided by the Branciard inequality and the Ozawa
inequality for some initial states and for particular class of joint
measurements under consideration. We also prove a modified form of Ozawa's
error-disturbance relation. The later relation provides a tighter bound
compared to the Ozawa and the Branciard inequalities for a small number of
states.
