People who have had skin cancer and avoid high-fat foods have a lower risk of the disease returning, according to a new study.

Reuters reports that an International Journal of Cancer study has linked a diet high in saturated, monounsaturated and polyunsaturated fats with an increased risk of developing squamous cell carcinoma.

Scientists followed 457 men and 600 women in a sub-tropical area of Australia with high exposure to ultraviolet sunlight for 11 years. They found that in the subjects with a prior history of skin cancer, higher total fat intake was associated with about a twofold increased risk of squamous cell cancer of the skin.

Subjects who did not have a previous history of skin cancer did not have an increased risk of skin cancer based on their diets, however.

Squamous cell carcinoma is the second most common type of skin cancer, according to the American Academy of Dermatology. It is considered treatable if it’s caught early.

Nutritional supplements containing vitamins C and E as well as selenium are also believed to help the skin fight cancer.