We give a method of construction of a hyper K-algebra on a set of order k, where k is a fixed cardinal number. Then we introduce the notion of quasi union hyper K-algebra and prove that any quasi union hyper K-algebra is implicative and whenever 0o0={0}, it is strong implicative hyper K-algebra. Also a quasi union hyper K-algebra is positive implicative if and only if it is a hyper BCK-algebra.