This paper deals with a new LMI-based observer design method for a class of nonlinear systems. Novel matrix multipliers are proposed to improve the feasibility of the LMI conditions existing in the literature. Two design procedures are proposed and both of them exploit a more general form of the matrix multiplier compared to the existing ones. The first method is based on the use of the standard Young relation jointly with a specific multiplier matrix, while the second one uses the LPV-based approach combined with a convenient Young inequality. The proposed LMIs contain additional numbers of decision variables as compared to the methods proposed in the literature, which add extra degrees of freedom thus improving the LMI feasibility. This is due to the use of a reformulated Lipschitz property and new matrix multipliers. Furthermore, the effectiveness of the proposed methodologies is highlighted through numerical comparisons.