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We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013 (Zangiabadi et al. in J Optim Theory Appl, 2013). In the earlier version, each iteration consisted of one socalled feasibility step and a few centering steps. Here, each iteration consists of only a feasibility step. Thus, the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step. The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.