This research article explores on metric, normal and division algebras and one of the objectives of this talk is to establish a fact that R, C and H are normal algebras .In this paper an innovative proof of a proposition namely “the metric algebra H2 is a normed algebra”, has been proposed. Besides a specific formula is evaluated for every differentiation of algebra. Furthermore an attempt has been made to present some fundamental characteristic properties of Cayley Algebra.The concepts namely doubling of algebras, metric algebras are discussed in an innovative way so that it shows a path to young researchers. They can have a glance on their future research by thinking over the phenomena namely structural constants of a Lie Algebra and the representation of the Lie Algebra by generators and relations.