In the context of the Transit Monitoring in the South project, we present nine new transit observations of the exoplanet OGLE-TR-113b observed with the Gemini South, Magellan Baade, Danish-1.54 m and Southern Astrophysical Research telescopes. We perform a homogeneous analysis of these new transits together with 10 literature transits to probe into the potential detection of an orbital decay previously reported for this planet. Our new observations extend the transit monitoring baseline for this system by 6 yr, to a total of more than 13 yr. With our timing analysis we obtained a dot{P}=-1.0 ± 6.0 ms yr-1, which rejects previous hints of a larger orbital decay for OGLE-TR-113b. With our updated value of dot{P} we can discard tidal quality factors of Q⋆ < 105 for its host star. Additionally, we calculate a 1σ dispersion of the transit timing variations of 42 s over the 13 yr baseline, which discards additional planets in the system more massive than 0.5-3.0 M⊕ in 1:2, 5:3, 2:1 and 3:1 Mean Motion Resonances with OGLE-TR-113b. Finally, with the joint analysis of the 19 light curves we update transit parameters, such as the relative semimajor axis a / R_s = 6.44^{+0.04}_{-0.05}, the planet-to-star radius ratio R_p / R_s =0.14436^{+0.00096}_{-0.00088}, and constrains its orbital inclination to i =89.27^{+0.51}_{-0.68} deg.