Suppose that \(f:\mathbb{B}^ n-\{0\} \to S^ n\) is a quasi-meromorphic mapping, where \(B^ n\) is the open unit ball in euclidean \(n\)-space and \(S^ n\) the unit sphere in euclidean \((n+1)\)-space. If 0 is an essential singularity then in every deleted neighbourhood of 0 there is an essential round sphere on which \(f\) assumes antipodal values. Thus if \[ \limsup_{| x |=| y |=r \to 0} q(f(x),f(y))<1, \] where \(q\) is the chordal metric normalised so that \(q(S^ n)=1\), then 0 is a removable singularity for \(f\).