The bank, which is part taxpayer-owned, will introduce a cap on mortgages worth more than £500,000, only allowing customers to borrow four times their income.
It is also limiting the loan period to a maximum of 30 years on large sums to prevent borrowers taking on more debt by spreading the repayments over longer periods.
Lloyds Banking Group has already introduced similar restraints. It is viewed as an extra safeguard on top of the affordability checks RBS has in place.
A spokeswoman said: "We are focused on looking after the interests of our customers and ensuring that they only take on mortgage lending that they can afford."
Britain's house prices rose at their fastest annual rate in nearly seven years last month, prompting concerns that some borrowers may be overstretching their finances.