40 pound in 4 weeks...that's 10 pounds a week.
It is possible, but is it probable?
In order for it to be probable, you need to be in the "obese" category, not simply overweight.
Obese = bodyfat of 32%+ for women (25%+ for men)
The more obese you are, the easier this task will be.
Restrict your caloric intake to 1,200 calories/day and do as much cardio each day as you can stand (at least 1 hour to burn 1 extra pound/week).
If you hit any plateaus, restrict your diet to only lean meats + veggies for 1-2 days.
For most people, a weight loss of 1-2 pounds/week is a reasonable and safe amount to shoot for, however if you absolutely must have 40 pounds in 4 weeks, be prepared to do a lot of cardio.
Your best bet though is to educate yourself further on what is and is not possible with a diet given your circumstances and learn how to set and achieve more manageable goals.