  We monitored the recent FUor 2MASS J06593158-0405277 (V960 Mon) since
November 2009 at various observatories and multiple wavelengths. After the
outburst by nearly 2.9 mag in $r$ around September 2014 the brightness gently
fades until April 2015 by nearly 1 mag in $U$ and 0.5 mag in $z$. Thereafter
the brightness at $\lambda>5000 \AA$ was constant until June 2015 while the
shortest wavelengths ($U, B$) indicate a new rise, similar to that seen for the
FUor V2493 Cyg (HBC722). Our near-infrared (NIR) monitoring between December
2014 and April 2015 shows a smaller outburst amplitude ($\sim$2 mag) and a
smaller (0.2 $-$ 0.3 mag) post-outburst brightness decline. Optical and NIR
color-magnitude diagrams indicate that the brightness decline is caused by
growing extinction. The post-outburst light curves are modulated by an
oscillating color-neutral pattern with a period of about 17 days and an
amplitude declining from $\sim$0.08 mag in October 2014 to $\sim$0.04 mag in
May 2015. The properties of the oscillating pattern lead us to suggest the
presence of a close binary with eccentric orbit.
