Social networking service has become very popular recently. Many recommendation systems have been proposed to integrate with social networking websites. Traditional recommendation systems focus on providing popular items or items posted by close friends. This strategy causes some problems. Popular items always occupy the recommendation list and they are usually already known by the user. In addition, items recommended by familiar users, who frequently communicate with the target user, may not be interesting. Moreover, interesting items from similar users with lower popularity are ignored. In this paper, we propose an algorithm, UBI, to discover unknown but interesting items. We propose three scores, i.e., Quartile-aided Popularity Score, Social Behavior Score, and User Similarity Score, to model the popularity of items, the familiarity of friends, and the similarity of users respectively in the target user's personal social network. Combining these three scores, the recommendation list containing unknown but interesting items can be generated. Experimental results show that UBI outperforms traditional methods in terms of the percentages of unknown and interesting items in the recommendation list.