A 4-0 thrashing of Rayo Vallecano at the weekend came on the back of an identical scoreline against the Dutch giants in midweek, allowing Martino to match the impressive start of his predecessor Tito Vilanova last season.
Few would bet against them adding another success at home to Real Sociedad on Tuesday and Martino is seeing signs of improvement in his team.
"I believe we are getting better," he said. "I would like to keep going along the way we played in the second halves against Ajax and Rayo. I feel we are getting there.
"I see the players more comfortable each day and think we are improving all the way. We have a perfect amount of points but are not close to perfection in our performances. We can keep improving; there are a lot of things we can do better."
Martino has announced a 19-man squad for the match, with Sergio Busquets recalled and Cesc Fabregas rested.
Real Madrid are only two points behind as they prepare to face Elche on Wednesday, but their more immediate concern is the fitness of world record signing Gareth Bale, who had to pull out of Sunday's 4-1 win over Getafe before kick-off with an injury.
Scans have revealed muscle fatigue, and while he is certain to miss the midweek match, it is unclear when he will return.
Barca are not alone in boasting a 100 per cent record as Atletico Madrid sit level at the top of the table thanks to the scintillating form of striker Diego Costa.
Tuesday's visit of a struggling Osasuna side should give them the chance to continue their own strong start.
Villarreal have cooled off with back-to-back draws but remain unbeaten and, just five games into their return to the top flight, are living it up like they used to in the top four.
There will be a good measure of how long they might be able to keep this form going when Espanyol, also enjoying an impressive start, are the visitors on Thursday.
Valencia endured a difficult start to the campaign but responded to a dismal 3-0 home loss to Swansea in the Europa League with a 3-1 victory over Sevilla on Sunday and will attempt to turn it into a fully-fledged revival away to Granada on Wednesday.
Sevilla, meanwhile, will hope to lift themselves off the foot of the table when they take on a Rayo side still reeling from that Barca drubbing.
Tuesday's fixtures are completed by Levante hosting Valladolid and Almeria travelling to Malaga.
On Thursday, Athletic Bilbao take on Real Betis, and Getafe are at home to Celta Vigo.