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In this paper, beamforming design is considered for a K-user multiple-input-multiple-output interference channel (MIMO-IC) under limited channel feedback budget at the users. Using a geometrical framework, an analytical expression for the upper bound on the total rate loss due to limited channel feedback is derived. The rate loss is a function of the total feedback budget available to the receiver, the strength of the desired and the interfering links at the users and the network parameters. This rate loss upper bound metric is then minimized at each receiver locally by allocating the feedback bits optimally among the links observed by it. We obtain an interesting result that under limited channel feedback budget at the users, interference alignment (IA) may not be the appropriate beamforming strategy. Based on the feedback bit allocation policy to minimize the rate loss upper bound at the receiver and the corresponding channel quantization error statistics at the transmitter, an improved beamformer design is proposed. The proposed beamformer shows a higher throughput gain compared to all other existing schemes.