In this work, we define the ultrahyperbolic Klein-Gordon operator of order α on the function f by T α ( f ) = W α ∗ f , where α ∈ C , W α is the ultrahyperbolic Klein-Gordon kernel, the symbol ∗ denotes the convolution, and f ∈ S , S is the Schwartz space of functions. Our purpose of this work is to study the convolution of W α and obtain the operator L α = T α − 1 such that if T α ( f ) = φ , then L α φ = f .