A new CMOS analog design methodology using an independently optimized self-cascode (SC) is proposed. This idea is based on the concept of the dual-workfunction-gate MOSFETs, which are equivalent to SC structures. The channel length of the source-side MOSFET is optimized, to give higher transconductance ($g_m$) and output resistance ($r_{out}$). The highest $g_m$ and $r_{out}$ of the SC structures are obtained by independently optimizing the channel length ratio of the SC MOSFETs, which is a critical design parameter. An operational amplifier (OPAMP) with the proposed design methodology using a standard digital $0.18-{mu}m$ CMOS technology was designed and fabricated, to provide better performance. Independently $g_m$ and $r_{out}$ optimized SC MOSFETs were used in the differential input and output stages, respectively. The measured DC gain of the fabricated OPAMP with the proposed design methodology was approximately 18 dB higher, than that of the conventional OPAMP.