A version of the secretary problem is considered. Items ranked from $1$ to $N$ are randomly selected without replacement, one at a time, and to win is to stop at any item whose overall (absolute) rank belongs to a given set of ranks. Only the relative ranks of the items drawn so far are observed. The analysis is based on the existence of an embedded Markov chain and uses the technique of backward induction. The requirement of choosing an item with a prescribed value of the absolute rank can lead to more complicated strategies than threshold strategies. This approach can be used to give exact results for any set of absolute ranks. Exact results for the optimal strategy and the probability of success are given for a few sets. These examples are chosen to illustrate the variety of character of optimal stopping sets. Asymptotic behaviour is also investigated.