An improvement for the large sieve for square moduli

We establish a result on the large sieve with square moduli. These bounds improve recent results by S. Baier [S. Baier, On the large sieve with sparse sets of moduli, J. Ramanujan Math. Soc. 21 (2006) 279–295] and L. Zhao [L. Zhao, Large sieve inequality for characters to square moduli, Acta Arith. 112 (3) (2004) 297–308].