My stepdaughter lies all the time, what should i do?

My 14 yr old stepdaughter lies all the time!!! Lies about every dum things AND steals. Once she stole my gold diamond rings from my jewel box and flashed one of them down into a toilet!! When she was caught, she lies about it, tiring to convince her dad that she didn't do anything. Well, he didn't buy that off course. We have 2 daughters, 5 and 1. My SD moved in our house about 2 years ago because, her mom married to a guy and my SD claimed that he touched her.(I doubt it) She obviously doesn't like my 5yrs old and says bad things about her (I happened to read some letters my stepdaughter wrote to her friends). We sat down and talk. I tried to be there when she needs some help. My husband did whatever it seemed good to stop her bad habit. BUT she doesn't stop lying and it's just getting sneaker. It's really bothers me when my SD acts so mean to my 5yrs daughter. I know I have to communicate but, I'm tired. I don't feel like talking to her or accusing her for her lies. Any suggestion?