J.A.Solinas suggested an optimal signed binary representation for pairs of integers, which is called a Joint Sparse Form (JSF). JSF is at most one bit longer than the binary expansion of the larger of the two integers, and the average joint Hamming density among Joint Sparse Form representations is 1/2. This paper extends the Joint Sparse Form by using a window method, namely a new representations, for pairs of integers, which is called Width-3 Joint Sparse Form (JSF₃). The representation is at most one bit longer than the binary expansion of the larger of the two integers, and the average joint Hamming density is 19/52. So, computing the form of uP+vQ by using JSF₃ is almost 9% faster than that by using JSF.