In this paper we establish a property of the binomial distribution This property refers to the conditional distribution ofY forX=x in the bivariate discrete distribution of (X, Y). It has been shown that when this conditional distribution is the convolution of a random variableX1 with the random variableX2, then the form of the joint distribution is uniquely determined by the marginal distribution ofX and the distribution of the convoluteX2. The distribution ofX1 is uniquely determined and is of the binomial form. We have established an equation connecting the joint distribution of (X, Y) with the marginal ofX and distributions ofX1 andX2.