I think on the surface you would have to agree that race relations between white and blacks have greatly improved over time. However I am sure there are still injustices done based on race in certain areas of the United States.
There have, of course, been many changes in race relations since 1940. The general trend has been for there to be less racial tension and more interaction between the races.
On an official level, race relations have improved tremendously. Things like the Brown decision from 1954 and the Civil Rights Act of 1964 have done away with almost all forms of legal discrimination.
On the personal level, things have changed as well. It is no longer socially acceptable to show overt racism in any setting. This constitutes a huge change from the 1940s when it was perfectly acceptable to oppose, for example, black and white children going to school or blacks playing sports with whites even at the professional level.