We know SGAN may have a risk of gradient vanishing. A significant improvement is WGAN, with the help of 1-Lipschitz constraint on discriminator to prevent from gradient vanishing. Is there any GAN having no gradient vanishing and no 1-Lipschitz constraint on discriminator? We do find one, called GAN-QP. To construct a new framework of Generative Adversarial Network (GAN) usually includes three steps: 1. choose a probability divergence; 2. convert it into a dual form; 3. play a min-max game. In this articles, we demonstrate that the first step is not necessary. We can analyse the property of divergence and even construct new divergence in dual space directly. As a reward, we obtain a simpler alternative of WGAN: GAN-QP. We demonstrate that GAN-QP have a better performance than WGAN in theory and practice.