This paper addresses less conservative control design for multiple design specifications. Problems are described by a set of linear matrix inequalities (LMIs) and solved with non-common LMI solutions in order to reduce the conservatism arising from seeking a common LMI solution in the past results. Noticing that completing the square can split two variables in bilinear matrix inequality (BMI) terms into two different LMI ones, we propose an iterative algorithm in which non-positive quadratic terms are successively replaced by their upper bounds. An illustrated example is included. Copyright (c) 2005 John Wiley & Sons, Ltd.