Your friend is probably talking about multiplayer Magic like Highlander that gives you one free mulligan.
Sanctioned tournament 2-player Magic still has the -1 card for each mulligan.
Refer to the Magic Comprehensive rules:
Comprensive Rule 103.4. excerpt wrote:
"...To take a mulligan, a player shuffles his or her hand back into his or her library, then draws a new hand of one fewer cards than he or she had before...."
Comprensive Rule 103.4c wrote:
"In a multiplayer game, the first time a player takes a mulligan, he or she draws a new hand of as many cards as he or she had before. Subsequent hands decrease by one card as normal."