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An extended form of beta distribution by Al-Saleh and Agarwal, is further extended which has an additional two shape parameters k and l. Introduction of new shape parameters help to express extended beta distribution not only as a mixture of distributions, but also provides extra flexibility to the density function over the interval [0,1]. Certain statistical properties such as the r-th moment are defined explicitly. Some of the shapes of family of the densities are also illustrated for different k and l so that it may help the Bayesians to approximate a wide range of prior beliefs among the members of the suggested extended family. The Bayesian analysis for the posterior of an uncertain parameter for the Bernoulli process using extended beta prior is also considered with an application of mortality rates in 12 hospitals performing surgery on babies.

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