The simple non-associative algebra

and its simple sub-algebras are defined in the papers [1], [3], [4], [5], [6], [12]. We define the non-associative algebra

and its antisymmetrized algebra

. We also prove that the algebras are simple in this work. There are various papers on finding all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [3], [5], [6], [9], [12], [14], [15]). We also find all the derivations

of te antisymmetrized algebra

and every derivation of the algebra is outer in this paper.