This note investigates observer design for a class of nonlinear one-sided Lipschitz stochastic systems with multiplicative noises. It is shown that the almost sure exponential convergence of the observation error could be treated by decoupling the state from this error. This is done by using a new theorem dedicated to triangular stochastic systems. The observer gains are designed using a polytopic technique exploiting the structure of the control inputs, coupled with a descriptor systems approach.