What was the name of the American TV show which presented a movie every night on New York's Channel 2 in the 1950s and early 1960s, right after the 11 p.m. news?

I don't have a specific link for this, but the national syndicated CBS movie was called simply "The Late Show".
http://www.youtube.com/watch?v=RNyIeFP-u3g
The theme played in the 50's and early 60's (and late 60's and early 70's) was The Syncopated Clock
https://en.wikipedia.org/wiki/The_Syncopated_Clock#The_Movie_Theme

In the early 70's the title was switched to "The CBS Late Movie" http://www.youtube.com/watch?v=0CfpCf-wWeY
But it was back being called "The Late Show" in the 1980's.

The Late Late show bumper (also used for just The Late Show too in the 70's and 80's)
http://www.youtube.com/watch?v=gL90PKbaClY
There was also a "Late Show 2" and a "Late Late Late Show"
for films shown after the 11:30 slot