1992 Dodge Shadow lighting system

Some cars allow for this to occur. To understand why this happens you will need to understand the wiring schematic for your particular vehicle. Basically the high beams have a separate switch which can be activated when the headlight switch is off (or no running lights while the car is on). Now if you are having a problem with the high beams always being on then that is something totally different. Is this your problem?

Reply to your answer where is the switch for the high beams located.I replaced the head light switch located in the dash board and still the high beams are on and the switch is off.

The high beam switch should be either mounted on the steering column (part of the turn signal switch), on the dash near the column, or lastly, a round switch on the floor panel. The last possibility is unlikely since this hasen't been used in over 25 years (for whatever reason they changed the design)