The author introduces a new bivariate beta distribution with joint probability density function, \[ f(x,y)= \frac{C x^{\beta -1}y^{\beta^\prime -1}{(1-x-y)^ {\gamma- \beta- \beta^\prime-1}}}{(1-u x-vy)^\alpha} \] for \( 0 < x < 1,~ 0 < y < 1, ~0< x + y < 1,~ \alpha, \beta, \beta^\prime > 0 \) and \( \gamma > \beta + \beta^\prime \) and obtains conditional, marginal densities and their moments.