The unique copula of a continuous random pair <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(X,Y)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> is said to be radially symmetric if and only if it is also the copula of the pair <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$(-X,-Y)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mi>X</mi> <mo>,</mo> <mo>-</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation>. This paper revisits the recently considered issue of testing for radial symmetry. Three rank-based statistics are proposed to this end which are asymptotically equivalent but simpler to compute than those of Bouzebda and Cherfi (J Stat Plan Inference 142:1262–1271, <CitationRef CitationID="CR1">2012</CitationRef>). Their limiting null distribution and its approximation using the multiplier bootstrap are discussed. The finite-sample properties of the resulting tests are assessed via simulations. The asymptotic distribution of one of the test statistics is also computed under an arbitrary alternative, thereby correcting an error in the recent work of Dehgani et al. (Stat Pap 54:271–286, <CitationRef CitationID="CR3">2013</CitationRef>). Copyright Springer-Verlag Berlin Heidelberg 2014
