Progressive Discipline for Discrimination

We have a situation between one worker who is of east Indian decent, and a second worker who is Caucasian. The Caucasian worker has put in a complaint that the worker of Wast Indian decent has made racial, and condescending comments towards them for having a different background and lesser working capabilities. After investigation on both sides, the East Indian worker denies any remarks, although discrimination has occurred in the plants before between other workers from both races, because of a heavy mixed culture environment. The East Indian worker has been investigated on two different occasions for accusations. We have made many efforts to educate and implement policies against discrimination and repercussions for doing so. How do we proceed with with disciplinary actions if the East Indian worker denies it, and we do not have any additional proof that it has occurred?