Yes, but there are special requirements for both the grantor and grantee foundation. The following is from our publication Legal Essentials for Private Foundations:
“Your foundation may wish to make grants to another private foundation or an organization controlled by your foundation for a charitable purpose. Such a grant will count as a qualifying distribution for your foundation if two requirements are met, in addition to exercising expenditure responsibility. First, the recipient foundation must meet its normal 5% distribution requirement for the year in which the grant is received, as well as the preceding year. After meeting both of these payout requirements, the recipient foundation must then expend the total amount of the grant from your foundation within 12 months after the end of the tax year in which it was received.”