This paper introduces a new way to synchronize clocks distanced apart and a way to synchronize clocks between reference frames. Based on a simple synchronization thought experiment, we claim that relativity of simultaneity must be incomplete. Einstein's special relativity theory predicts relativity of simultaneity and that two events that happen simultaneously in one reference frame will not happen simultaneously as observed from another reference frame. Relativity of simultaneity is directly linked to a particular way of synchronizing clocks (Einstein-Poincar\'{e} synchronization) that again assumes that the one-way speed of light is isotropic and identical with the well-tested round-trip speed of light. In the new thought experiment introduced here, there is reason to believe that two distant events can happen simultaneously in both frames. Still, we agree that these events will not happen simultaneously as measured with Einstein synchronized clocks. The claim here is that Einstein synchronized clocks lead to apparent relativity of simultaneity due to a clock synchronization error rooted in the assumption of isotropic one-way speed of light.