Two avors of the recommendation problem are the explicit and the implicit feedback settings. In the explicit feedback case, users rate items and the user item preference relationship can be modelled on the basis of the ratings. In the harder but more common implicit feedback case, the system has to infer user preferences from indirect information: presence or absence of events, such as a user viewed an item. One approach for handling implicit feedback is to minimize a ranking objective function instead of the conventional prediction mean squared error. The naive minimization of a ranking objective function is typically expensive. This difficulty is usually overcome by a trade-off: sacrificing the accuracy to some extent for computational efficiency by sampling the objective function. In this paper, we present a computationally effective approach for the direct minimization of a ranking objective function, without sampling. We demonstrate by experiments on the Y!Music and Netix data sets that the proposed method outperforms other implicit feedback recommenders in many cases in terms of the ErrorRate, ARP and Recall evaluation metrics.