Shapefile Issue

Hi all,


Ok, so I'm a little old to ArcGIS and I'm slowly trying to relearn it all. Recently I was adding a shapefile from someone else in my office and I noticed that the shapefiles were off just little bit on top of the USGS maps layer. How would I transform that layer into one that fits completely on the map. Is it something to do with 1927 coordinates and 1983 coordinates?


Thanks,

Matthew