Source : Webster's Revised Unabridged Dictionary (1913)

Self-assured \Self`-as*sured`\, a.
   Assured by or of one's self; self-reliant; complacent.

Source : WordNet®

self-assured
     adj : showing poise and confidence in your own worth; "hardly more
           than a boy but firm-knit and self-confident" [syn: {self-confident}]