Given a sequence of orthogonal polynomials {𝐿𝑛}∞𝑛=0 , orthogonal with respect to a positive Borel 𝜈 measure supported on ℝ+ , let {𝑄𝑛}∞𝑛=0 be the the sequence of orthogonal polynomials with respect to the modified measure 𝑟(𝑥)𝑑𝜈(𝑥) , where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula 𝑄(𝑑)𝑛(𝑧)𝐿(𝑑)𝑛(𝑧)⇉𝑛∏𝑁1𝑘=1(𝑎𝑘√+𝑖𝑧√+𝑎𝑘√)𝐴𝑘∏𝑁2𝑗=1(𝑧√+𝑏𝑗√𝑏𝑗√+𝑖)𝐵𝑗 , on compact subsets of ℂ∖ℝ+ , where 𝑎𝑘 and 𝑏𝑗 are the zeros and poles of r, and the 𝐴𝑘 , 𝐵𝑗 are their respective multiplicities.