A web site usually contains a large number of concept entities, each consisting of one or more web pages connected by hyperlinks. In order to discover these concept entities for more expressive web site queries and other applications, the web unit mining problem has been proposed. Web unit mining aims to determine web pages that constitute a concept entity and classify concept entities into categories. Nevertheless, the performance of an existing web unit mining algorithm, iWUM, suffers as it may create more than one web unit (incomplete web units) from a single concept entity. This paper presents a new web unit mining algorithm, kWUM, which incorporates site-specific knowledge to discover and handle incomplete web units by merging them together and assigning correct labels. Experiments show that the overall accuracy has been significantly improved.