Abstract Let X 1, X 2,… be i.i.d. random variables with continuous distribution function F < 1. It is known that if 1 - F( x) varies regularly of order - p, the successive quotients of the order statistics in decreasing order of X 1,…, X n are asymptotically independent, as n→∞, with distribution functions x kp , k = 1, 2, …. A strong converse is proved, viz. convergence in distribution of this type of one of the quotients implies regular varation of 1 - F( x).