Saccharomyces cerevisiae repressor-activator protein 1 (Rap1) is an essential protein involved in multiple steps of DNA regulation, as an activator in transcription, as a repressor at silencer elements, and as a major component of the shelterin-like complex at telomeres. All the known functions of Rap1 require the known high-affinity and specific interaction of the DNA-binding domain with its recognition sequences. In this work, we focus on the interaction of the DNA-binding domain of Rap1 (Rap1(DBD)) with double-stranded DNA substrates. Unexpectedly, we found that while Rap1(DBD) forms a high-affinity 1:1 complex with its DNA recognition site, it can also form lower-affinity complexes with higher stoichiometries on DNA. These lower-affinity interactions are independent of the presence of the recognition sequence, and we propose they originate from the ability of Rap1(DBD) to bind to DNA in two different binding modes. In one high-affinity binding mode, Rap1(DBD) likely binds in the conformation observed in the available crystal structures. In the other alternative lower-affinity binding mode, we propose that a single Myb-like domain of the Rap1(DBD) makes interactions with DNA, allowing for more than one protein molecule to bind to the DNA substrates. Our findings suggest that the Rap1(DBD) does not simply target the protein to its recognition sequence but rather it might be a possible point of regulation.