  We probe the properties of the transient X-ray pulsar MAXI J1409$-$619
through \textit{RXTE} and \textit{Swift} follow up observations of the outburst
in 2010. We are able to phase connect the pulse arrival times for the 25 days
episode during the outburst. We suggest that either an orbital model (with
$P_{{\rm{orb}}} \simeq 14.7(4)$ days) or a noise process due to random torque
fluctuations (with $S_r \approx 1.3 \times 10^{-18}$ Hz$^2$ s$^{-2}$ Hz$^{-1}$)
is plausible to describe the residuals of the timing solution. The frequency
derivatives indicate a positive torque-luminosity correlation, that implies a
temporary accretion disc formation during the outburst. We also discover
several quasi-periodic oscillations (QPOs) in company with their harmonics
whose centroid frequencies decrease as the source flux decays. The variation of
pulsed fraction and spectral power law index of the source with X-ray flux is
interpreted as the sign of transition from a critical to a sub-critical
accretion regime at the critical luminosity within the range of $6\times
10^{37}$ erg s$^{-1}$ to $1.2\times 10^{38}$ ergs s$^{-1}$. Using
pulse-phase-resolved spectroscopy, we show that the phases with higher flux
tend to have lower photon indices, indicating that the polar regions produce
spectrally harder emission.
