In 2002, H.H. Chan, K.S. Chua and P. Solé found that for each positive integer d, there are theta series A d , B d and C d of weight one that satisfy the Pythagoras-like relation A 2 d = B 2 d + C 2 d . In this article, we show that there are two collections of theta series A b,d , B b,d and C b,d of weight one which satisfy A 2 b,d = B 2 b,d + C 2 b,d , where b and d are certain integers.