Term Life Insurance for my sister and me?

Can I buy a term life insurance policy on my sister and name myself as beneficiary without telling her about the policy? Her son, my only nephew, would be 2nd beneficiary should I die first. I plan to do the same thing for myself, naming my sister as 1st beneficiary. Nothing sinister here at all. We are the only 3 surviving relatives and we have no funeral coverage or death benefits of any sort.