In his six years as coach, the Argentine has brought back the open, attacking football which characterised Colombia in the 1990s but has also given it a more dynamic edge.
Pekerman became a national hero in the country after leading Colombia to their best-ever World Cup performance in 2014 when they were one of the most exciting teams at the tournament.
It seemed that, after several false dawns, Colombia had established themselves as one of the world's top 10 teams.
But since then they have moved sideways rather than forwards and performances have been generally disappointing.
Colombia did just enough in the World Cup qualifiers to claim fourth spot in the South American group, although they only scored 21 goals and limped over the line with three draws and a defeat in their final four games.
Their scoring problem is particularly baffling given an abundance of forwards such as Teo Gutierrez, Duvan Zapata, Carlos Bacca and Luis Muriel.
Performances at the Copa America in 2015, when they lost to Argentina on penalties in the quarter-finals, and the Copa Centenario in 2016, when they failed to muster a goal in the quarter-final or semi-final, were also uninspiring.
Pekerman's cause has not been helped by James Rodriguez's problems at club level after his move to Real Madrid backfired.
Top scorer at the 2014 World Cup, Rodriguez was consigned to the bench for most of the last two seasons and has played only seven Bundesliga games since joining Bayern Munich this season.
On the other hand, forward Radamel Falcao has rediscovered his scoring touch at AS Monaco, Juan Cuadrado is always a handful on the flank and there are new talents such as defenders Davinson Sanchez and Yerry Mina.
The World Cup is littered with cases of teams who have struggled through qualifying and performed well at the finals and it is quite possible Colombia will click when it matters.
(Writing by Brian Homewood; editing by Ken Ferris)