The current goal of exoplanetary science is not only focused on detecting but characterizing planetary systems in hopes of understanding how they formed, evolved, and relate to the solar system. The Transit Ephemeris Refinement and Monitoring Survey (TERMS) combines both radial velocity (RV) and photometric data in order to achieve unprecedented ground-based precision in the fundamental properties of nearby, bright, exoplanet-hosting systems. Here we discuss HD 6434 and its planet, HD 6434b, which has a M_p_sini=0.44M_J_ mass and orbits every 22.0170 days with an eccentricity of 0.146. We have combined previously published RV data with new measurements to derive a predicted transit duration of ~6 hr, or 0.25 days, and a transit probability of 4%. Additionally, we have photometrically observed the planetary system using both the 0.9 and 1.0m telescopes at the Cerro Tololo Inter-American Observatory, covering 75.4% of the predicted transit window. We reduced the data using the automated TERMS Photometry Pipeline, developed to ensure consistent and accurate results. We determine a dispositive null result for the transit of HD 6434b, excluding the full transit to a depth of 0.9% and grazing transit due to impact parameter limitations to a depth of 1.6%.