Transmission congestion is one of the key factors to local market power in competitive electricity markets. Financial transmission rights provide the financial protection to their holders by paying back the congestion rent. A variety researches have shown that the existing trading mechanisms on transmission right can exacerbate market power. This paper proposes an alternative methodology in mitigating the local market power using the Contingent Transmission Rights on the locational marginal pricing scheme. The proposed methodology was demonstrated with the Optimal Power Flow.