Interacting selectively and non-covalently with DNA containing the crossed form of a four-way junction, also known as a Holliday junction, a structure where two DNA double strands are held together by reciprocal exchange of two of the four strands, one strand each from the two original helices. The crossed form of a four-way junction cannot be diagrammed without any of the strands crossing over, and instead contains a single crossover between two of the strands.