Rotation coefficients for overlap integrals over arbitrary atomic orbitals are calculated by two methods. In the first method, using binomial coefficients, directly calculated Clebsch-Gordan coefficients and normalized associated Legendre functions were used to obtain the rotation coefficients. Whereas in the second method recursively calculated Clebsch-Gordan coefficients and normalized associated Legendre functions were used. The methods are compared with respect to cpu time requirement and accuracy. It was concluded that it is appropriate to use the first method for angular momentum quantum numbers up to 40 and for larger quantum numbers the second method is more advantageous. Keywords: Overlap integrals, rotation of overlap integrals, Clebsch-Gordan coefficients, associated Legendre functions ; Rotation coefficients for overlap integrals over arbitrary atomic orbitals are calculated by two methods. In the first method, using binomial coefficients, directly calculated Clebsch-Gordan coefficients and normalized associated Legendre functions were used to obtain the rotation coefficients. Whereas in the second method recursively calculated Clebsch-Gordan coefficients and normalized associated Legendre functions were used. The methods are compared with respect to cpu time requirement and accuracy. It was concluded that it is appropriate to use the first method for angular momentum quantum numbers up to 40 and for larger quantum numbers the second method is more advantageous. Keywords: Overlap integrals, rotation of overlap integrals, Clebsch-Gordan coefficients, associated Legendre functions