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We derive a new inequality that is necessary and sufficient to showEPR-steering in a scenario employing only correlations between two arbitrarydichotomic measurements on each party. Thus the inequality is a completesteering analogy of the CHSH inequality, a generalisation of the result ofCavalcanti et al, JOSA B, 32(4), A74 (2015). We show that violation of theinequality only requires measuring over equivalence classes of mutuallyunbiased measurements on the trusted party and in fact assuming a general twoqubit system arbitrary pairs of distinct projective measurements at the trustedparty are equally useful. Via this it is found that for a given state themaximum violation of our EPR-steering inequality is equal to that for the CHSHinequality, so all states that are EPR-steerable with CHSH-type correlationsare also Bell nonlocal.

All two-qubit states that are steerable via Clauser-Horne-Shimony-Holt-type correlations are Bell nonlocal