AmaZulu are set to face Richards Bay FC in the Last 16 of the Ke Yona Cup at the Umhlathuze Sports Complex on Friday, with a place in the last eight at stake.
"We do have character of late. We have been showing good signs, though we are still a work in progress," Zwane said.
"We are looking to improve in each and every game. Hopefully, we will treat this match with the respect it deserves and progress to the next round. But it won't be easy, just like the last game we played in Polokwane."
Coming up against familiar opposition, Zwane has paid close attention to Richards Bay's recent performances and believes they pose a serious threat.
"I am not playing games when I say Richards Bay have been doing very well," he told journalists this week.
"If you look at where they are and how they have been performing lately, you will see what I am talking about.
"Against Chippa United, tactically in the first half, they could have scored three goals in the opening 10 minutes alone. In the game before that, they actually scored three."