  We give a sufficient condition under which vanishing property of
Cochran-Orr-Teichner knot concordance obstructions splits under connected sum.
The condition is described in terms of self-annihilating submodules with
respect to higher-order Blanchfield linking forms. This extends results of
Levine and the authors on distinguishing knots with coprime Alexander
polynomials up to concordance. As an application, we show that the knots
constructed by Cochran, Orr and Teichner as the first examples of nonslice
knots with vanishing Casson-Gordon invariants are not concordant to any knot of
genus one.
