A nonlocal square root of the Klein-Gordon equation is proposed. This
nonlocal equation is a special relativistic equation for a scalar fiel
d of first order in the time derivative. Its space derivative part is
described by a pseudodifferential operator. The usual quantum mechanic
al formalism can be set up. The nonrelativistic limit and the classica
l limit in the form of plane wave solutions and the Ehrenfest theorem
are correctly included. The nonlocality of the wave equation does not
disturb the light cone structure, and the relativity principle of spec
ial relativity is fulfilled. Uniqueness and existence of solutions of
the Cauchy problem for this equation can be proved. The second quantiz
ed version of this theory turns out to be macrocausal.