A basic double series is expressed in terms of two 5ϕ4 series which extends Bailey's transformation of an 8ϕ7 series into two 4ϕ3 's. From this formula we derive some quadratic transformations; one of them is a new q-analogue of a transformation due to Whipple. Product formulas as well as Gasper-Rahman's q-Clausen formula are also given as special cases.