The current Honda City does not have any diesel-CVT combination although the newly debuted Amaze will get this configuration. As strange as it sounds, there are solid reasons for Honda choosing not to introduce this configuration for the present generation Honda City at present. The current generation is likely to be phased out within a year or a little more time and the company does not think it feasible to introduce this configuration at this stage of the product lifecycle.
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However, reports state that the next generation Honda City could get the diesel-CVT combination. The 5th generation City model in India will draw inspiration from the newly launched Insight and Accord models by way of design. Expect more features like curtain airbags, a brand new touchscreen infotainment system and new safety features. These changes will help the next generation City to compete better with rivals like the Hyundai Verna and upcoming Toyota Yaris.