The generalized Chaplygin gas model with parameter space \alpha > -1 is studied in this paper .
Some reasonable physical constraints are added to justify the use of the larger parameter space .
The Type Ia supernova data and age data of some clusters are then used to fit the model .
We find that the parameters have bimodal distributions .
For the generalized Chaplygin gas model , we also find that less free parameters fit the data better .
The best fit model is the spatially flat model with baryons .
The best fit parameters are : \Omega _ { m 0 } = 0.044 , w _ { c 0 } = -0.881 and \alpha = 1.57 .
The transition redshift is z _ { T } = 0.395 .