In this paper we show that an arbitrary contractive projection on a /*-algebra has the properties of a conditional expectation (Theorem 1). This fact is then used to solve the bicontractive projective problem (Theorem 2). Let M be a /*-algebra and let θ be an isometry (equivalently a /*-automorphism [7]) of M of order 2. Then P, defined by Px = ^(x + θx), is a bicontractive projection on M9 i.e., P2 = P9 \\P < 1, ||idM - < 1. By the bicontractive projection problem we mean the converse of this statement. An affirmative answer to the bicontractive projection problem imposes strong symmetry properties on the Banach space M, so it cannot be true for a general Banach space. In Bernau-Lacey [2], the problem is solved for the class of Lindenstraus spaces. In [1] Arazy-Friedman solved it with M = the C*-algebra of compact operators on a separable complex Hubert space. In [10], StΘrmer, influenced by partial results of Robertson-You ngson [9], solved it with M an arbitrary C*-algebra and P assumed positive and unital. Our Theorem 2, specialized to a C*-algebra, generalizes each of these results of Arazy-Friedman and StΘrmer. The authors have recently solved the problem for associative Jordan triple systems [3].